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Active Materials for Functional Origami

Advanced Materials

December 2023
36(9):e2302066

DOI:10.1002/adma.202302066

Authors:

Sophia Leanza

Stanford University

Shuai Wu

Stanford University

Xiao-Hao Sun

Georgia Institute of Technology

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In recent decades, origami has been explored to aid in the design of engineering structures. These structures span multiple scales and have been demonstrated to be used towards various areas such as aerospace, metamaterial, biomedical, robotics, and architectural applications. Conventionally, origami or deployable structures have been actuated by hands, motors, or pneumatic actuators, which can result in heavy or bulky structures. On the other hand, active materials, which reconfigure in response to external stimulus, eliminate the need for external mechanical loads and bulky actuation systems. Thus, in recent years, active materials incorporated with deployable structures have shown promise for remote actuation of light weight, programmable origami. In this review, active materials such as shape memory polymers and alloys, hydrogels, liquid crystal elastomers, magnetic soft materials, and covalent adaptable network polymers, their actuation mechanisms, as well as how they have been utilized for active origami and where these structures are applicable is discussed. Additionally, the state‐of‐the‐art fabrication methods to construct active origami are highlighted. The existing structural modeling strategies for origami, the constitutive models used to describe active materials, and the largest challenges and future directions for active origami research are summarized. This article is protected by copyright. All rights reserved

Introduction to traditional, engineering, and active origami. a) Schematic of traditional origami crane folding process. b) Different types of common engineering origami such as the Miura–ori pattern and associated metamaterials (Adapted with permission.[⁵] Copyright 2015, National Academy of Sciences); flasher origami pattern and deployable solar array (Reproduced with permission from the authors).[¹⁸] waterbomb base origami pattern and waterbomb tube biomedical stent (Reproduced with permission from the authors).[¹²] c) Representation of common actuation strategies for active origami, including heating of LCE hinges (Adapted with permission.[³³] Copyright 2017, The Royal Society of Chemistry); heating of SMP hinges (Adapted with permission.[³⁵] Copyright 2014, IOP Publishing); heating of hydrogel to expel water at hinges (Adapted with permission.[³⁰] Copyright 2014, IOP Publishing); applied external magnetic field to actuate a magnetized MSM (Adapted with permission.[³⁷] Copyright 2018, Springer Nature). d) Additional common origami mechanisms, including instability‐based origami such as the Kresling pattern (Reproduced with permission.[⁷³] Copyright 2020, National Academy of Sciences); curved‐crease origami (as compared to straight‐crease origami) (Adapted with permission.[⁹⁸] Copyright 2020, the Authors, some rights reserved; exclusive licensee AAAS); pop‐up origami initiated by a stretched kirigami substrate and maintained by an elastic layer of material (Adapted with permission.[¹⁰¹] Copyright 2019, Elsevier).

…

Hinge design and considerations for origami structures. a) Hinges for conventional paper‐based origami that are introduced by creasing a sheet. b) Several methods to generate compliant hinges for origami with finite thickness including reduced thickness at the hinge, cuts introduced at the hinge, or reduced material stiffness at the hinge. c) Mechanisms for actuation when active materials are introduced to the structure.

…

SMP mechanism, origami, and applications. a) Shape memory effect of an amorphous SMP. b) One‐way shape memory process of an SMP box upon heating (Adapted with permission.[¹¹⁵] Copyright 2010, Wiley). c) Self‐folding of pre‐stretched sheets by local light absorption (Adapted with permission.[¹³⁹] Copyright 2012, The Royal Society of Chemistry). d) Self‐folding of layered structures with prescribed folding angle under uniform heating (Adapted with permission.[¹¹⁶] Copyright 2014, IOP Publishing). e) Sequentially folded and locked box by hinges of different Ttrans under uniform heating (Adapted with permission.[¹¹⁷] Copyright 2015, Springer Nature). f) Hydrogel‐SMP composite structures with reversible actuation (Adapted with permission.[²⁰⁴] Copyright 2016, Springer Nature). g) Magnetic SMP gripper with locking capabilities (Adapted with permission.[²⁰⁷] Copyright 2020, Wiley). h) SMP Kresling‐based metamaterial with tunable mechanical properties (Adapted with permission.[¹²⁷] Copyright 2020, Elsevier).

…

Hydrogel actuation mechanism, origami, and applications. a) Hydrogel actuation mechanism: swelling, de‐swelling. b) Reversible folding and un‐folding of a box with hydrogel at the hinges (Reproduced with permission.[¹⁴⁸] Copyright 2011, American Chemical Society). c) Micro‐scale trilayer origami with complex deformation (Adapted with permission.[¹⁴⁷] Copyright 2015, Wiley). d) Hydrogel gripper capable of locomotion and cell capture/excision (Adapted with permission.[¹⁶¹] Copyright 2015, American Chemical Society). e) Hydrogel actuator with synergistic deformation and color change (Adapted with permission.[¹⁵²] Copyright 2018, Wiley). f) Hydrogel robot with octopus‐like locomotion (Adapted with permission.[²³⁷] Copyright 2021, Elsevier). g) Hydrogel metamaterials with negative swelling behavior (Adapted with permission.[¹⁵⁹] Copyright 2018, the Authors, some rights reserved; exclusive licensee AAAS).

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LCE actuation mechanism and origami. a) Nematic (ordered) to isotropic (disordered) transition of LCEs. b) Macroscopic deformation of LCE according to common mesogen alignments (Adapted with permission.[²⁶³] Copyright 2020, AIP Publishing). c) Optimal hinge design for LCE box and folding of LCE upon heating (Adapted with permission.[¹⁷¹] Copyright 2015, The Royal Society of Chemistry). d) Deployment of reconfigurable structure by actuation of LCE fibers (Reproduced with permission.[¹⁷⁹] Copyright 2022, Wiley). e) Multimaterial origami airplane structure with LCE actuators triggered by Joule heating (Adapted with permission.[⁰³³] Copyright 2017, The Royal Society of Chemistry). f) Pop‐up of a liquid metal (LM)‐LCE composite triggered by induction heating (Adapted with permission from the authors).[¹⁸¹] g) LCE origami with synergistic shape and color change (Reproduced with permission.[¹⁶⁸] Copyright 2021, Wiley). h) Self‐propelled LCE rolling robot (Adapted with permission.[¹⁷²] Copyright 2019, AAAS).

…

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REVIEW

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Active Materials for Functional Origami

Sophie Leanza, Shuai Wu, Xiaohao Sun, H. Jerry Qi, and Ruike Renee Zhao*

In recent decades, origami has been explored to aid in the design of

engineering structures. These structures span multiple scales and have been

demonstrated to be used toward various areas such as aerospace,

metamaterial, biomedical, robotics, and architectural applications.

Conventionally, origami or deployable structures have been actuated by

hands, motors, or pneumatic actuators, which can result in heavy or bulky

structures. On the other hand, active materials, which reconﬁgure in response

to external stimulus, eliminate the need for external mechanical loads and

bulky actuation systems. Thus, in recent years, active materials incorporated

with deployable structures have shown promise for remote actuation of light

weight, programmable origami. In this review, active materials such as shape

memory polymers (SMPs) and alloys (SMAs), hydrogels, liquid crystal

elastomers (LCEs), magnetic soft materials (MSMs), and covalent adaptable

network (CAN) polymers, their actuation mechanisms, as well as how they

have been utilized for active origami and where these structures are

applicable is discussed. Additionally, the state-of-the-art fabrication methods

to construct active origami are highlighted. The existing structural modeling

strategies for origami, the constitutive models used to describe active

materials, and the largest challenges and future directions for active origami

research are summarized.

1. Introduction

The art of paper folding transforms 2D sheets into 3D architec-

tures, with the earliest paper folding being traced to 1st century

China when the papermaking process was invented. Origami, the

Japanese paper folding art, began from the 6th century and grad-

ually developed into more meticulous designs, such as the well-

known paper crane (Figure 1a). Origami has remained popular

over the years as a form of art, while it has also become a promi-

nent scientiﬁc topic, also referred to as engineering origami

S. Leanza, S. Wu, R. R. Zhao

Department of Mechanical Engineering

Stanford University

Stanford, CA 94305, USA

E-mail: rrzhao@stanford.edu

X. Sun, H. J. Qi

The George W. Woodruﬀ School of Mechanical Engineering

Georgia Institute of Technology

Atlanta, GA 30332, USA

The ORCID identiﬁcation number(s) for the author(s) of this article

can be found under https://doi.org/10.1002/adma.202302066

DOI: 10.1002/adma.202302066

(Figure 1b), with great relevance to the

ﬁelds of mathematics and mechanics.

Its capability of transforming a 2D sheet

into a complicated 3D shape or reshap-

ing a deployed structure into a compact

folded state attracts signiﬁcant attention

and development in diﬀerent engineer-

ing ﬁelds and research areas, including

aerospace structures,[1,2 ] metamaterials,[3–7]

robotics,[8,9,10,11 ] biomedical devices,[12,13 ]

reconﬁgurable electronics,[14–16 ] and

architecture,[5,17 ] encompassing a wide

range of length scales, at which pre-

stresses or actuators are built into the

origami system to facilitate the folding.

As mechanical properties of origami are

tunable by the geometrical parameters

of the origami pattern, structures with

versatile mechanical properties such as

metamaterials can be designed (Figure 1b,

left).[5] Properties of origami such as the

auxetic nature of Miura–ori or variable stiﬀ-

ness during folding have been utilized for

metamaterial applications.[3,5 ] In aerospace

applications, a signiﬁcant change in size

from the deployed to folded conﬁgurations

is necessary for eﬃcient storage and/or

transportation of structures such as solar arrays (Figure 1b,

middle),[1,18,19 ] space habitats,[20] and bellows.[21] Through fold-

ing, origami-based aerospace structures can exhibit such im-

mense changes in size, and origami patterns such as the

ﬂasher, Miura–ori, and Yoshimura have been commonly demon-

strated for this purpose. In addition, origami has been used

for biomedical applications where tools or devices capable

of folding and reconﬁguration can aid in or improve cer-

tain procedures, such as deployable origami stents (Figure 1b,

right),[12] origami forceps,[22] and origami-inspired surgical

robots.[23]

While the foldability and shape reconﬁgurability of origami of-

fers signiﬁcant reconﬁguration of structures, the conventional

methods to actuate the shape change has largely relied on me-

chanical loads provided by hands, motors,[24–26 ] or pneumatic

pumps.[4,11,27–29 ] However, the use of manual loading for engi-

neering applications is often impractical, while motors and pneu-

matically driven systems are often bulky and require complicated

control, especially for high degrees-of-freedom (DOF) actuation.

On the other hand, active materials reconﬁgure in response to ex-

ternal stimuli, eliminating the need for external mechanical loads

and bulky actuation systems.

In recent decades, active materials, also referred to as stimuli-

responsive or smart materials, provide alternative strategies for

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Figure 1. Introduction to traditional, engineering, and active origami. a) Schematic of traditional origami crane folding process. b) Diﬀerent types

Academy of Sciences); ﬂasher origami pattern and deployable solar array (Reproduced with permission from the authors).[18] waterbomb base origami

pattern and waterbomb tube biomedical stent (Reproduced with permission from the authors).[12] c) Representation of common actuation strategies for

Additional common origami mechanisms, including instability-based origami such as the Kresling pattern (Reproduced with permission.[73] Copyright

the Authors, some rights reserved; exclusive licensee AAAS); pop-up origami initiated by a stretched kirigami substrate and maintained by an elastic

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the actuation of reconﬁgurable systems. These materials and

their composites with functional groups/ﬁllers show response to

external stimuli including light, heat, electric or magnetic ﬁelds,

and pH. Utilizing active materials, for instance, shape memory

polymers (SMPs) and alloys (SMAs), hydrogels, liquid crystal

elastomers (LCEs), magnetic soft materials (MSMs), and cova-

lent adaptable network (CAN) polymers, conventional origami

has been advanced to active origami.[1,30–36 ] These origami sys-

tems actuated by stimuli-responsive materials have the advan-

tages of being less bulky, as they do not require motors or

other external actuators, light weight, programmable (and of-

tentimes re-programmable), remotely controllable or tetherless

in many cases, as well as capable of selective or distributed ac-

tuation. These merits can enable applications in remote or bi-

ological spaces where conventionally actuated systems are less

viable. To illustrate how these materials generally operate, sev-

eral examples of active origami are shown in Figure 1c, in

which a box with LCE at its hinges can be folded when heat

is applied, causing the LCE to contract.[33] Similarly, a pyra-

mid structure is actuated by its SMP hinges upon heating,[35] a

hydrogel-based pyramid can fold when water is expelled from

its hinges,[30] and a Miura–ori patterned MSM with embed-

ded magnetic particles and precisely programmed magnetization

aligns its magnetization with an external magnetic ﬁeld and thus

folds.[37]

Given many excellent recent reviews on stimuli-responsive

materials and their applications,[38–44 ] origami-inspired func-

tional designs,[7,45–48 ] and origami modeling,[49] this review will

focus on summarizing the recent advances in origami systems

that are enabled by active materials. We will qualitatively dis-

cuss the diﬀerent origami mechanisms, material types and their

actuation mechanisms, and advanced manufacturing of active

origami systems and their applications. Section 1 brieﬂy summa-

rizes the common origami mechanisms and diﬀerent hinge de-

sign strategies for the structural implementation of origami, fol-

lowed by the actuation mechanisms of active materials and their

applications in Section 2. In Section 3, manufacturing methods

for active origami systems are introduced, including molding,

additive manufacturing, and micro/nano-scale fabrication. Next,

theoretical frameworks including both structural modeling and

material constitutive laws that guide the design of active origami

are brieﬂy reviewed in Section 4. Lastly, in Section 5, we provide

a discussion on the challenges and outlooks for the ﬁeld of active

origami.

1.1. Origami Mechanisms

In this section, diﬀerent mechanisms which facilitate reconﬁg-

uration of origami structures are discussed, starting from clas-

sic origami patterns, and then moving on to discuss origami

based on instability, curved-crease origami, and pop-up origami.

It should be noted that certain types of origami fall under sev-

eral of these categories. Additionally, “kirigami”, or the art of pa-

per folding where cuts are permitted, is inherently very closely

tied to the art of origami. It is common for these two arts to be

discussed in tandem,[7,45,46,50–53 ] especially when discussing real-

world applications of origami which require more sophisticated

structural designs and functional materials.

1.1.1. Classic Origami Patterns

Origami patterns transform between their folded and deployed

states through rigid body rotation of panels, which are connected

by hinges. Conventional origami patterns do not require bend-

ing, twisting, or stretching of panels, for example, Miura–ori,[54]

waterbomb,[55,56 ] Tachi–Miura polyhedron,[57] stacked Miura–

ori patterns,[5,58 ] square-twist,[59] Yos h i m u r a , [60] and Ron Resch

origami.[61,62 ] In real paper-based or polymer-based origami

structures, however, deformation occurs most at the hinges while

panel deformation can also occur. This enlarges the origami

design space for patterns such as Kresling,[63–65 ] ﬂasher,[1,18]

and hypar origami,[66,67 ] and allows for higher DOF shape

morphing.[68]

1.1.2. Origami based on Instability

Instabilities are commonly utilized in the folding and deploy-

ment of origami structures. Kresling origami,[69,70 ] for example,

whose pattern is generated from the twist buckling of thin cylin-

drical shells, can be designed to be monostable or bistable. Bista-

bility or multistability of other patterns such as the hypar[66] or

square-twist[59,71 ] can be reached when allowing for panel bend-

ing. Another way that multi-stable origami structures have been

achieved is via stacking of patterns. For example, the stacking of

Miura–ori sheets yields a structure with multiple stable states.[72]

In a similar way, stacked Kresling units have been demonstrated

intensively as multistable structures (Figure 1d, top),[73,74] loco-

motive robots,[75] and metamaterials.[65] Multistable structures

have the advantages of not requiring constant external force or

stimulus for folding/deployment and can additionally allow for

programmable stiﬀness of structures[73] or can be used for me-

chanical memory applications.[25,76 ]

Additional examples of reconﬁgurable structures based on

instability can be found in slender structures. Examples in-

clude buckling of thin strips or patterned sheets to generate

3D architectures,[77–79 ] snap buckling of twisted rods to looped

conﬁgurations,[80] and twisting of composite structures with pre-

stressed ﬂanges.[81] A related topic is ring origami,[82–85] or slen-

der ring structures capable of folding via buckling instability

when loads are applied. Those studied recently have been gener-

alized to multiple diﬀerent ring geometries, follow a self-guided

snap-folding mechanism, and have been demonstrated for fold-

able trusses and devices.[86–90 ]

1.1.3. Curved-Crease Origami

Curved-crease origami was ﬁrst documented in the 1930s[91]

and then expanded to various patterns by artists, for example,

concentric circles[92] and pleated hyperbolic paraboloid,[66,93] in

which introduced curved creases distinguish them from the

straight creases seen with conventional origami patterns (see

Figure 1d, middle).[98] Elastic deformations in both the hinges

and panels during the folding of curved-crease origami are es-

sential and can lead to complex energy landscapes which are

worth exploring for engineering design. While studies on curved-

crease origami have largely been related to the mathematics of

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Figure 2. Hinge design and considerations for origami structures. a) Hinges for conventional paper-based origami that are introduced by creasing a

sheet. b) Several methods to generate compliant hinges for origami with ﬁnite thickness including reduced thickness at the hinge, cuts introduced at

the hinge, or reduced material stiﬀness at the hinge. c) Mechanisms for actuation when active materials are introduced to the structure.

describing diﬀerent curved-crease patterns,[52] recent studies en-

compass engineering applications as well, with topics including

metamaterials,[94] membranes for aerospace structures,[95] adap-

tive shading systems,[96] high-strength performance foldcores,[97]

and robotic grippers with programmable stiﬀness and snapping

behaviors.[98]

1.1.4. Pop-Up Origami

An additional type of origami, pop-up origami, is characterized

by 2D sheets that can “pop up”/assemble to 3D conﬁgurations.

Pop-up origami is most often achieved through the release of pre-

stressed substrates to trigger out-of-plane deformation of thin

sheets to a variety of diﬀerent 3D states.[77,99,100 ] Other pop-up

origami, however, can be triggered by multistability or plastic-

ity of kirigami patterns paired with elastic materials (Figure 1d,

bottom),[101 ] external mechanical loading of kirigami,[102 ] lam-

ination of layered sheets,[103 ] or ion beam irradiation of thin

metal ﬁlms.[104 ] While pop-up origami is applicable to many

size scales, it has shown especial promise for the fabrication of

small-scale electronics,[105 ] biomedical devices,[23,106 ] and recon-

ﬁgurable robots[107–109 ] with complex geometries.

1.2. Structural Implementation of Origami

For conventional paper-based origami, creases are introduced by

plastically deforming the sheet (Figure 2a). The creases, whose

stiﬀness is lower than the undeformed panels, serve as the

hinges about which the panels rotate so that diﬀerent conﬁgura-

tions of the origami can be realized. While paper-based origami

has been widely used for artistic purposes and for some addi-

tional small-scale electronic or sensing applications,[110–112 ] many

other practical applications of origami, however, involve mate-

rials with more appreciable thickness. Because of this, there

have been many works to address the structural design of

origami that accounts for the panel and hinge thickness.[113,114,18 ]

Thus, to enable folding of these more broadly encompassed

origami structures, tactics are needed to generate compliant

hinges. As depicted in Figure 2b, reduction in thickness at

the hinge, introduction of cuts at the hinge, or introduction

of a lower-stiﬀness material at the hinge are all methods that

make folding possible for these origami structures (see Sec-

tion 4.1 for details on structural modeling of origami). Start-

ing from a structure with the compliant hinge design, there

are several hinge actuation mechanisms enabled by the incor-

poration of active materials that result in the desired folding

of an active origami structure (Figure 2c). By either introduc-

ing a bilayer hinge with a contractible material on top, a bi-

layer hinge with an expandable material on the bottom, or an

inactive hinge attached to active panels capable of generating

torques (most common with MSMs), the same general upward

folding of the panels can be achieved once the active mate-

rial is actuated. From here, it can be seen that there is a con-

siderable design space for structural implementations of active

origami.

2. Active Materials for Origami Actuation

Table 1 summarizes the main active materials that will be dis-

cussed in this review, along with the stimulus that leads to the

actuation, the mechanism by which these materials operate, a

broad summary of performance details such as actuation speed

and stiﬀness of the materials, and the applications that these

active origami systems have been designed for. The details of

these diﬀerent active origami will be discussed in their respective

sections.

2.1. Shape Memory Polymers (SMPs)

SMPs can be programmed into temporary shapes and recover

their permanent shape upon external stimuli, such as heat, light,

or magnetic ﬁeld. The shape of SMPs can be changed and

easily recovered, enabling a wide variety of uses in deployable

aerospace structures,[193 ] biomedical applications,[194 ] and ﬂexi-

ble electronics.[195 ] SMPs have the ability to be programmed into

arbitrary shapes and to maintain this temporary shape at ambi-

ent conditions. In addition, for amorphous polymer-based SMPs,

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Table 1. Summary of active materials, actuation mechanisms, performance details, and applications.

Material Actuation stimulus Actuation Mechanism Performance Details Applications

Shape memory

polymers (SMPs)

Heat[1,35,115–136 ]

Light[137–143 ]

Humidity[144,145 ]

Chemical[141 ]

Release of pre-stress at

hinges[1,35,115–136,138–145 ]

Moderate actuation time

(s–min)

Higher stiﬀness and

actuation stress (MPa–GPa)

Oftentimes only have

one-way actuation

Biomedical[131,132 ]

Aerospace structures[1,126,128 ]

Energy harvesting[130 ]

Shock absorption[127,129 ]

Hydrogels Water[59,146,147]

Heat[59,147–152 ]

Light[148,153,154 ]

pH[152,155–157 ]

Ionic strength[156,157 ]

Swelling at bilayer

hinge[59,146–149,151,152,154–157 ]

Swelling with

porosity gradient[153 ]

Swelling with

crosslinking

gradient[155 ]

Slow actuation (min–hrs)

Lower stiﬀness and

actuation stress (kPa)

Reversible deformation

Operate in aqueous

environments

Metamaterials[158,159 ]

Drug delivery robots[160 ]

Cell encapsulation or excision

robots[161–164 ]

Liquid crystal

elastomers (LCEs)

Heat[33,165–173 ]

Humidity[174,175 ]

Light[176,177 ]

Bilayer hinges[33,177 ]

Fiber actuation at

hinges[33,178–180 ]

Twisted nematic or

splayed hinges[171,173 ]

Fast actuation (ms–s)

Moderate stiﬀness and

actuation stress (kPa–MPa)

Reversible deformation

Biomimetic actuators[165,168 ]

Locomotive robots[168,172,181 ]

Magnetic soft

materials (MSMs)

Magnetic ﬁeld[31,37,182–189 ] Body torque of

panels[37,182–186,188–192 ]

Fast actuation (ms–s)

Material properties depend

on matrix material

Reversible deformation

Tetherless actuation

Drug delivery[75]

Biomimetic robots[75,183 ]

Robots for object

transportation[31,183,186 ]

Metamaterials[187,189 ]

their elastic modulus can shift by nearly three to four orders of

magnitude before and after their glass transition.[196 ] This high

modulus (oftentimes on the scale of a few GPa) at low tempera-

tures can oﬀer the advantage of load-carrying capabilities. In ad-

dition, the actuation of SMPs typically takes several seconds to

several minutes.[193,197,198 ]

2.1.1. Shape Memory Mechanism

From a mechanistic point of view, SMPs are network polymers

composed of switching segments (molecular chains) and net-

points (chemical or physical crosslinks),[198 ] as indicated by the

blue lines and black dots, respectively, in Figure 3a. These poly-

mers have a transition temperature (Ttrans)suchasaglasstran-

sition (Tg)ormelting(Tm) temperature, above which the mate-

rial will be programmable. A typical shape memory cycle involves

two steps. In the ﬁrst step (or the programming step), the SMP is

heated to above Ttrans. It becomes rubbery, exhibits an increase in

chain mobility, and can be easily deformed into a programmed

shape. As the deformation is maintained and the temperature is

lowered to below Ttrans, the segments become frozen and main-

tain their deformed chain conﬁgurations as well as the deformed

shape of the SMP. This state is commonly referred to as the tem-

porary shape. During the second step (or the recovery step), the

SMP is heated above its Ttrans again, during which the polymer

chains regain mobility and entropy drives the polymer back to

its permanent shape. An example of the process is shown in

Figure 3b,[115] where an SMP box programmed to be temporar-

ily open (Figure 3b-i) gradually returns to its permanent folded

shape (Figure 3b-ii) upon heating. It should be noted that, for

most SMPs, this is a one-way shape memory process: the SMP

cannot shift between two shapes as it is heated and cooled, and

it must be mechanically programmed again to exhibit another

cycle of the shape memory eﬀect. Two-way shape memory, a re-

versible process in which the material can switch back and forth

between two shapes by heating above and cooling below Ttrans is

also achievable, but typically requires special design of polymer

composites or macromolecular structures.[199–201 ] It should also

be mentioned that multi-shape-SMPs[202,203 ] are those which can

switch between more than two shapes and can be obtained by

using multiple transition temperatures and programming steps.

2.1.2. SMP Origami

Depending on the Ttrans of the material, SMP-based ac-

tive origami has the advantage of maintaining its tempo-

rary shape at ambient conditions. One way that SMPs have

been used to achieve active origami is to utilize pre-stretched

sheets.[116,125,133,138–140,143 ] Since these sheets begin as pre-

stretched, they are initially in their “temporary” shapes and, upon

heating, they relax and thus contract. Origami constructed of

these sheets was ﬁrst demonstrated by Liu et al.,[139 ] where black

ink (serving as hinges) was printed on either side of a polystyrene

(an SMP) sheet. Under IR light, the black ink absorbed light

and transferred heat to the SMP underneath, causing a tem-

perature gradient through the thickness of the ﬁlm to result in

bending toward the ink-patterned side. Thus, by patterning ink

on either side of the ﬁlm, unidirectional or bidirectional folding

(Figure 3c) was achieved under the stimulus of unfocused light.

Folding structures such as a box, pyramid, and bidirectional fold-

ing strips were demonstrated with this approach, and similar ap-

proaches were used later on.[138,140,143 ] Tolley et al.[116] developed

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Figure 3. SMP mechanism, origami, and applications. a) Shape memory eﬀect of an amorphous SMP. b) One-way shape memory process of an SMP

one-way SMP origami structures with predictable folding angles

by placing the SMP sheet between two stiﬀ paper layers, with

the hinges located at the gaps between paper layers (Figure 3d-i).

When heated, the sheet contracted, causing bending at the

hinges, which ceased when the panels were in contact with one

another, resulting in a controlled bending angle (Figure 3d-ii).

With this approach, they demonstrated the folding of a polyhe-

dron, Miura–ori (Figure 3d-iii), and various other origami struc-

tures.

While the hinges discussed above exhibit the same general re-

sponse to a homogeneous stimulus, hinges can also be designed

to fold sequentially and enable complex folding routines. Mao

et al.[117 ] used SMPs with diﬀerent glass transition temperatures

to design hinges and achieved sequentially self-folding and self-

locking structures. They demonstrated a folding box (Figure 3e),

which requires sequential actuation of hinges to avoid interfer-

ence or collision of panels during the folding process. Guided

by ﬁnite element analysis (FEA) simulations and a reduced or-

der model to predict collision of panels during folding, SMP

hinges of three diﬀerent Ttrans were chosen, in which fast-folding

hinges had low Ttrans and slow-folding hinges had high Ttrans,to

enable the sequential folding of a self-locking box (Figure 3e).

This work emphasized the importance of the planning of fold-

ing sequence in complex active origami structures. Other ap-

proaches have also been taken to achieve sequential folding. For

example, by using the same material as that in their initial[139 ]

work, Liu et al.[140 ] later achieved sequential folding by using

hinges of diﬀerent colored inks that absorbed IR light with dif-

ferent eﬃciency, allowing for sequential folding of a variety of

structures.

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As discussed previously, most SMPs cannot achieve reversible

actuation. Therefore, active origami that solely uses SMPs can-

not typically have desirable reversible folding and unfolding.

One way to realize reversibly foldable active origami is through

SMP composites, in which another active material drives (or pro-

grams) the shape change while the SMP locks it. Mao et al.[204 ]

demonstrated this concept with structures composed of a hydro-

gel, an elastomer, and an SMP. As seen in Figure 3f-i, a struc-

ture was designed with an SMP top layer, elastomer side and bot-

tom layers, and hydrogels conﬁned by columns between the top

and bottom layers. Upon swelling in water and heating to soften

the SMP layer, the structure bent toward the elastomer layer. The

structure was then cooled to stiﬀen the SMP and thus lock the

temporary shape. After drying of the hydrogel, the locked shape

was still maintained. The original shape of the structure could

be recovered by heating it again, allowing the SMP to return to

its equilibrium shape. This process could be repeated, enabling

reversibly foldable and un-foldable SMP composite structures

(Figure 3f-ii). Recently, this approach was further developed by

simply using an SMP/hydrogel bilayer to enable reversible shape

change by Yuan et al.[205]

Magnetic particles have also been used to establish similar

functionality in SMPs. This type of material capable of reversible

shape transformation has been termed as magnetic SMP (M-

SMP). Photothermally heated M-SMP and inductively heated M-

SMP have been developed by Liu et al.[206 ] and Ze et al.,[207 ] re-

spectively. In the work by Ze et al.,[207 ] an M-SMP with two diﬀer-

ent types of magnetic particles (NdFeB and Fe3O4) was created.

The Fe3O4particles enabled inductive heating of the SMP under

a high frequency alternating current (AC) magnetic ﬁeld (heating

magnetic ﬁeld), while magnetized NdFeB particles drove shape

change of the SMP by aligning the polymer’s magnetization di-

rection to an actuation magnetic ﬁeld. When the heating mag-

netic ﬁeld was turned on, the M-SMP became soft and could

easily be deformed into a desirable shape by the actuation mag-

netic ﬁeld. Further, by keeping the actuation magnetic ﬁeld on

but ceasing the heating magnetic ﬁeld, the M-SMP cooled down

until it stiﬀened. After the actuation magnetic ﬁeld was turned

oﬀ, the temporary shape was ﬁxed, and this method was demon-

strated for the use of a soft gripper (Figure 3g). The incorporation

of SMP with other active materials such as LCEs has also been

demonstrated recently,[208] and it can be seen that SMP compos-

ites allow for various interesting deformations and functionali-

ties.

SMPs enable a wide variety of applications, across many diﬀer-

ent ﬁelds of research. One application of SMPs has been active

metamaterials,[119,125,129,209 ] which can exhibit special mechanical

properties. For example, Tao et al.[127] designed SMP Kresling-

based metamaterials in which temperature could be used to con-

trol the load bearing and energy absorption capabilities of the

structures. As shown in Figure 3h, structures could be designed

to fold in sequential ways due to the geometry of the Kresling

origami used, which could be utilized for impact mitigation or

soft robotic applications. Recently, biocompatible shape mem-

ory materials such as keratin[210 ] have also been explored for ac-

tive origami, potentially for use as smart textiles. Chen et al.[1]

demonstrated the use of SMPs in facilitating the deployment

of ﬂasher origami solar arrays for potential aerospace applica-

tions. Additionally, SMPs have been used for other exciting ap-

plications such as robotic joints with tunable stiﬀness,[211,212 ]

deployable origami sandwich structures,[126 ] origami reﬂector

antennas,[128 ] carbon nanotube (CNT)-SMP-based foldable solar

evaporators,[130 ] and origami biomedical devices.[131,132 ]

2.2. Hydrogels

Hydrogels are network polymers that can absorb large amounts

of water. Some hydrogels can exhibit macroscopic deformation by

absorbing (swelling) or expelling (de-swelling) water in response

to changes in stimulus such as heat, pH change, ionic strength,

and light. The stiﬀness and actuation stress of hydrogels typically

lie between a few kPa to several hundred kPa.[213,214] Hydrogel ac-

tuation is slow, as it is driven by a diﬀusion process. This results

in hydrogel actuation occurring anywhere from tens of minutes

to several hours. Storage of elastic potential energy,[215] utiliza-

tion of instabilities,[216 ] incorporation of particles for hydrogel

composites,[148,153 ] or conﬁned swelling environment for reten-

tion of high osmotic pressures[217 ] have all been taken advantage

of for increasing either the actuation speed, force, or mechanical

strength of hydrogels. Due to their low elastic modulus compa-

rable to biological materials and tissue,[218 ] hydrogels are often

used for biomedical applications, such as patches[219 ] and drug

delivery.[160] Hydrogels are also used in soft robotics including

biomimicking systems,[220 ] locomotive robots,[221–223 ] as well as

active origami.[147,148,156 ]

2.2.1. Hydrogel Mechanism

In general, hydrogel swelling or de-swelling is due to the inter-

action between the polymer chains and the surrounding solvent

molecules. In a good solvent, in which the interaction between

the polymer chains and the solvent is preferred, polymer chains

are arranged as hydrophilic “coils” and the hydrogel can absorb

solvent (such as water). On the other hand, in a poor solvent,

in which the interaction between polymer chains with one an-

other is preferred, polymer chains become hydrophobic “glob-

ules” and the solvent will be expelled. Under diﬀerent conditions

such as varied temperatures or pH, a solvent can be good or poor

with respect to the polymer chains, leading to a volume phase

transition of the hydrogel.[224,225 ] For example, some hydrogels,

such as poly(N-isopropylacrylamide) (pNIPAM), will repel water

once heated above the hydrogel’s lower critical solution temper-

ature (LCST) and the hydrophilic coils will become hydropho-

bic globules (Figure 4a). It is important to note that swelling of

neat hydrogels is isotropic, so to achieve more complex defor-

mation necessary for origami, tactics such as varied crosslinking

densities,[150,226 ] porosity gradients,[153 ] or structures such as bi-

layers of materials with diﬀerent swelling capabilities,[147,161,227 ]

are often used. Among these tactics, bilayers are the overwhelm-

ingly popular method for the creation of hydrogel hinges for

origami.

2.2.2. Hydrogel Origami

Bilayer-based hinge design typically consists of a layer of ac-

tive material and a layer of inactive material, or two active

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Figure 4. Hydrogel actuation mechanism, origami, and applications. a) Hydrogel actuation mechanism: swelling, de-swelling. b) Reversible folding

rights reserved; exclusive licensee AAAS).

materials with diﬀerent stimuli-responsiveness. For example,

Zhang et al.[148 ] used a hinge consisting of a layer of pNI-

PAM hydrogel and a layer of low-density polyethylene (LDPE)

for diﬀerent origami structures (Figure 4b). To simplify the

fabrication, hydrogel was only used in the patterned hinge re-

gions. They further loaded CNTs in the hydrogel to tune the re-

sponse time and to allow for near-IR irradiation-induced fold-

ing. Many other materials such as graphene oxide or reduced

graphene oxide,[152,153,228–230 ] MoS2,[ 154 ] and clay[151,157,228 ] have

also been incorporated with hydrogels to enhance the response

time and/or mechanical properties. It should be noted that other

various demonstrations of bilayer hydrogel origami have been

conducted by Ionov and coworkers, who have studied self-rolling

bilayer ﬁlms[227 ] which can fold to 3D structures[149,216 ] such as

pyramids.

While the abovementioned bilayer origami is relatively simple,

multi-layered designs have also been used to enable more com-

plex hydrogel origami.[59,147 ] Na et al.[147 ] demonstrated micro-

scale origami with controlled mountain and valley folds with a

three-layer design: a thermoresponsive hydrogel layer between

two rigid polymer layers patterned with crease lines for either

mountain folds or valley folds. Upon immersion in water be-

low the LCST, the origami self-folded to its complex micro-scale

shape (Figure 4c), while it nearly reversibly returned to its origi-

nal conﬁguration when heated above the LCST. They also demon-

strated the folding of a tessellation with 198 patterned creases

(Figure 4c). Although the origami shown is very impressive, it is

important to note that such complex self-folding origami can suf-

fer from mis-folding,[116,231 ] resulting in ﬁnal conﬁgurations that

are diﬀerent from the desired ones. To address this issue, the

same group used hydrogels with two diﬀerent LCSTs, patterned

in a way such that the vertices of a complex origami design could

be pre-biased[232 ] toward certain directions, allowing for more re-

liable sequential folding of the origami creases to the desired ﬁnal

3D shape.

As mentioned previously, hydrogels have been widely used for

biomedical applications. Self-rolled tubes for vascularization[233]

as well as numerous grippers[30,161,162,234 ] for drug delivery or

cell removal (biopsy) in surgical applications have been demon-

strated with hydrogels. Notably, Gracias and coworkers[161,162 ]

have created origami microgrippers by incorporating stiﬀ poly-

mer panels with a thermoresponsive hydrogel substrate, where

the stiﬀness of the panels granted additional functionality to the

gripper, such as the possibility of cell excision. Grippers were

able to locomote[161 ] via the incorporation of magnetic particles

into the hydrogel layer, allowing remote control by a magnetic

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probe. Cell excision was accomplished by placing the grippers in

a warm environment with cell tissue. Starting in a closed con-

ﬁguration, upon heating, the gripper opened up and folded in

the opposite direction, grasping a portion of tissue (Figure 4d)

and excising the cells from the tissue upon full closure of the

gripper. Additionally, drug delivery[162] from the grippers was

demonstrated by the incorporation of drugs into the layers of the

gripper. Other origami-like approaches to drug delivery[160] and

cell/particle encapsulation[163,164 ] using hydrogels have been ex-

plored as well.

Aside from biomedical applications, hydrogels are also perti-

nent to biomimetic applications, with some hydrogels exhibit-

ing synergistic ﬂuorescent color and shape change.[152,235 ] Ma

et al.[152 ] designed a bilayer gripper (Figure 4e) with the bottom

side as a thermoresponsive hydrogel. At high temperatures, the

bottom layer expelled water and this led to downward bending,

exhibiting a ﬂuorescent top layer under the green light. Upon a

decrease in temperature, however, the actuator would bend up-

ward and the color would change as a result. Another exciting

and recent example of biomimetic origami was the utilization

of hydrogel on a polydimethylsiloxane (PDMS) substrate with

microﬂuidic channels.[220 ] The device could respond to tempera-

ture, light, and humidity for an environmentally responsive actu-

ator with plant-like movements and photosynthesis capabilities.

Lastly, light-actuated hydrogel origami[230,236,237] has enabled soft

robots capable of crawler and octopus-like[237 ] motions. By utiliz-

ing bilayers composed of spiropyran functionalized with photo-

contracting and photo-expanding hydrogel, Li et al.[237 ] achieved

large bending deformation. By integrating the bilayers with ratch-

eted feet for anisotropic friction with a substrate, they achieved

biomimetic, octopus-like motions (Figure 4f) upon repeated re-

laxing and contraction of the bilayers.

Additional hydrogel origami applications entail metama-

terials with negative swelling enabled by positive-swelling

hydrogel.[159,238 ] Zhang et al.[159 ] utilized hydrogel to achieve

metamaterials with negative swelling (Figure 4g) by adjusting the

initial geometry of the metamaterial units. In changing the unit

geometries, metamaterials with expansion in one direction and

contraction in the orthogonal direction were achieved, demon-

strating interesting mechanical properties. Also, hydrogel for the

assembly of 3D, origami-like structures used for acoustic meta-

materials has been demonstrated by Deng et al.[158 ]

2.3. Liquid Crystal Elastomers (LCEs)

LCEs are a class of active materials that exhibit large,

reversible[239 ] deformation upon exposure to stimuli such

as heat,[240,241 ] light,[242,243 ] solvents,[ 244] electric,[ 245,246 ] or

magnetic[247 ] ﬁelds. LCEs are elastomers which have elon-

gated, anisotropic mesogens (typically composed of rigid

aromatic or cyclohexyl rings[248,249 ]) ﬁxed to the polymer main

chain or sidechains by covalent bonds and crosslinks.[248 ] The

ﬂexible nature of the elastomer allows for changes in the or-

dering of the mesogens upon stimuli, along with reversible

actuation.[250,251 ] Mesogens in LCEs are programmed to have

long-range orientational order described by a director, which

means that it has a high level of molecular order similar to that of

a crystalline solid, while maintaining ﬂuidity similar to a viscous

liquid.[252 ] LCEs can exhibit mechanical, optical, electrical, and

magnetic anisotropic properties[248,253 ] in their ordered, or most

commonly “nematic”, state and isotropic behaviors in their dis-

ordered, or “isotropic”, state.[248 ] Due to their ease of reversible

deformation and large actuation strain, LCEs are used for a

number of applications, including artiﬁcial muscles[239,241,254 ]

and smart textiles.[255 ] Additionally, because the actuation of

LCEs is a phase transition process not governed by diﬀusion,

LCEs can actuate in several seconds, or even in a fraction of a

second.[181,256 ] The stiﬀness of LCE and the actuation stress, on

the other hand, usually range from hundreds of kPa to several

MPa.[241,256,257]

2.3.1. LCE Mechanism

The actuation of LCEs is due to the transition from a liquid

crystalline phase, such as nematic or smectic, to an isotropic

phase in response to a stimulus (typically temperature) that dis-

rupts mesogen alignment (Figure 5a). For most LCEs, there

exists a phase transition temperature referred to as the ne-

matic to isotropic phase transition temperature (TNI). Applica-

tion of an appropriate stimulus leads to a contraction paral-

lel to the director of the LCE.[239,258 ] Upon heating, polymer

chains gain entropy and become more coiled, causing mesogens

to lose their alignment and become randomly oriented, result-

ing in a macroscopic shrinkage of the LCE.[249,250,259 ] Thus, the

alignment and orientation of mesogens in LCEs are of critical

consideration in LCE applications. Previously, mesogens were

commonly aligned via surface rubbing[260 ] or electric ﬁelds,[261]

which are relatively tedious methods. More recently, a two-step

reaction method developed by Yakacki et al.[262 ] is often used,

which ﬁrst involves a thiol-Michael addition “click” reaction

to form the polydomain LCE (or LCE without long-range or-

der), followed by alignment of mesogens by stretching, and ﬁ-

nal locking of the alignment via photopolymerization reaction.

Planar nematic, twisted nematic, and splay are common liq-

uid crystal orientations for LCEs. Twisted and splay orientations

(Figure 5b)[263] involve variations in the director through the

thickness of the material, allowing for more complex deforma-

tion. In twisted and splay orientations, there exists a 90-degree

rotation of the director through the material thickness. Twisted

orientation involves an in-plane rotation of the director while

splayed is out-of-plane. When an appropriate stimulus is ap-

plied, mismatches in the expansion of the surfaces leads to bend-

ing/folding behaviors.[244,264 ] Because of this, diﬀerent mesogen

orientations can be exploited for origami-like deformations of

materials.

2.3.2. LCE Origami

Thermo- and light- responsive LCEs comprise the majority of

LCE origami works, although it should be noted that humid-

ity and water-stimulated folding of LCE-based structures is also

achievable, often via bilayers,[265 ] alkaline,[174 ] or acidic[ 175] sur-

face treatment to enable asymmetric humidity response. White,

Ware, and collaborators have done a series of works related to

the folding of LCE. In a seminal work, they enabled the program-

ming of complex director orientations into thin LCE via surface

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Figure 5. LCE actuation mechanism and origami. a) Nematic (ordered) to isotropic (disordered) transition of LCEs. b) Macroscopic deformation of

LCE composite triggered by induction heating (Adapted with permission from the authors).[181 ] g) LCE origami with synergistic shape and color change

alignment, in which local twisted nematic alignments were ef-

fectively deﬁned as the origami hinges.[173 ] Upon heating, the

ﬂat sheet would fold into Miura–ori. However, a downside was

the lack of control over folding upon heating. They later used

the same surface alignment technique and developed a topol-

ogy optimization[171 ] method to generate more reliable hinge

designs, with an aim to avoid anti-clastic, saddle-like curvature

seen in the actuation of twisted nematic LCEs.[264,266,267 ] Their

optimal hinge involved programmed triangular regions near the

substrate’s corners (Figure 5c-i) with approximately twisted ne-

matic order patterned through the thickness for nearly com-

plete closure of the box upon heating (Figure 5c-ii). They fur-

ther used LCE-CNT composites[176 ] as the hinges to enable a

light-activated LCE folding box that took advantage of CNT pho-

tothermal eﬀects. Lastly, Donovan et al.[ 268] demonstrated a long-

lasting folded LCE box by incorporating o-ﬂuorinated azoben-

zene into the polymer network. The trans-to-cis isomerization

of the o-ﬂuorinated chromophores resulted in directional strains

on the LCE and allowed for the macroscopic deformation, which

could last for multiple days. This type of prolonged deformation

of LCE can be beneﬁcial, as a constant stimulus would typically

be needed for LCE to maintain its deformation, which may un-

necessarily consume energy. This topic will be discussed further

in Section 2.5.

Other origami-like folding of ﬂat sheets to 3D shapes has been

achieved by introducing complex LCE director distributions re-

alized by photoaligned substrates or molds with micrometer-

scale channels.[269–272 ] Another more simpliﬁed approach was to

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program the folding of bilayer origami LCE sheets by spraying

LCE onto thermoplastic sheets, as demonstrated by Verpaalen

et al.[177 ] Upon thermally shaping and ﬁxing the sheets, sharp,

origami-like folds could be introduced. These thin bilayer strips

were actuated by UV and blue light and simple deformation from

accordion to ﬂower-like shape was demonstrated.

Instead of designing LCE origami based on entire sheets of

LCE, axially aligned LCE ﬁbers, or strips of LCE that contract

along their length when actuated, can also be selectively placed

among origami structures to generate folding.[178–180,33 ] As seen

in Figure 5d, Peng et al.[179] printed LCE ﬁbers onto a square-

shaped reconﬁgurable structure. When the structure was loaded,

it fell to a parallelogram-like shape that could be deployed back

to the initial state upon heating the ﬁbers. In their work, they

also demonstrated deployment of a printed tensegrity structure

and reconﬁguration of an LCE lattice pyramid. An additional ad-

vantage of the use of LCE ﬁbers/strips compared to LCE sheets

is that they can be selectively actuated by methods such as Joule

heating, which can enable more complicated folding routines. By

using LCE ﬁbers as the actuators, Yuan et al.[33] demonstrated

a variety of multimaterial origami structures composed of an

elastomeric material (Tangoblack by Stratasys (Rehovot, Israel)),

a rigid polymer (Verowhite by Stratasys), and a conductive ink.

They obtained an inactive substrate by inkjet printing and then

printed conductive ink onto this substrate via direct ink writing

(DIW), after which they incorporated the LCE strips into the pre-

determined positions atop the ink. Under an applied current, the

conductive ink was Joule heated, leading to the actuation of the

origami. Once the current was ceased, the LCE cooled down and

the actuator gradually returned to its original ﬂat state. An air-

plane actuator, as seen in Figure 5e, utilized LCE ﬁbers on the top

and bottom sides to serve as actuators for upward and downward

bending, respectively. Miura–ori, as well as a sequential folding

box were also demonstrated with this method.

While sequential or selective actuation (and thus folding) of

LCE origami can be obtained from Joule heating, a limitation of

this is that wires are often needed to supply current, which com-

plicates the structure. In a recent work, Maurin et al.[181 ] devel-

oped liquid metal (LM)-LCE composites that could be remotely

heated by induction under alternating magnetic ﬁelds. The heat-

ing of LCE was concentrated in regions where the LM was lo-

cated, and the LM could be patterned arbitrarily due to the LM-

spraying method that was used. By varying the quantity of LM

and the LM pattern, as well as the alignment of LCE and the mag-

nitude of the applied magnetic ﬁeld, the actuated shape of the

LCE could be programmed. As shown in Figure 5f, an LCE sam-

ple with circumferential alignment (which buckles out of plane

when actuated[173 ]) and LM throughout the composite sequen-

tially “pops up” under an increasing magnetic ﬁeld, where the

centermost LCE buckles ﬁrst, followed by the outermost LCE. In

their work, the LM-LCE composite was also used to design sea-

turtle-inspired actuator “ﬁns” for a biomimetic turtle robot.

Eﬀorts have also been taken to realize color change during

the actuation of LCE origami.[165,168 ] Huang et al.[ 168] recently

presented luminescent LCE origami by incorporating ﬂuores-

cent and color-changing agents into the LCE matrix, includ-

ing a blue-green ﬂuorescent moiety tetraphenylethene, a pho-

tochromic moiety spiropyran, and an NIR photothermal dye

YHD796. NIR light was used as a heat source to facilitate the

deformation of the LCE, while UV and visible light were used

for reversible color change between green-blue and red at folded

states and dull red at deployed states (Figure 5g). Both Miura–

ori and Yoshimura origami were demonstrated by introducing

folds mechanically, creating a gradient of mechanical stress that

allowed for reversible folding and unfolding. By controlling the

applied light, synergistic shape and color change of the origami

was achieved, enabling biomimetic behaviors such as camouﬂag-

ing.

LCE-based active origami has also been used to generate lo-

comotion for robotics applications. Kotikian et al.[172 ] assembled

multiple diﬀerent examples of LCE origami, taking advantage

of thermoresponsive LCEs with diﬀerent nematic to isotropic

transition temperatures. They utilized rigid acrylate panels with

LCE bilayer hinges. The hinges involved two LCE layers printed

orthogonal to one another to enable large bending curvatu res

(up to 180 degrees). To achieve sequential folding, they strate-

gically used hinges with LCEs of either high TNI or low TNI

throughout their designs, and demonstrated sequentially fold-

able structures, as well as a self-propelling, rolling robot, as

shown in Figure 5h. This robot utilizes low TNI (blue) hinges

to gradually fold the body into a pentagonal prism and high

TNI (orange) hinges to propel the robot forward, allowing for

continual rolling motion. Upon activation by a hot plate, the

hinges provide torques which sustain the forward motion of

the robot, even after undergoing a full revolution. Other works

have demonstrated locomotion via LCE actuation for crawling[273]

origami robots. Additional exciting LCE origami applications

include thermoresponsive LCE kirigami metasurfaces[274 ] and

LCE metamaterials demonstrated as shrinkable patches for skin

regeneration.[275 ]

2.4. Magnetic Soft Materials (MSMs)

MSMs are a class of active materials that permit fast, reversible,

and untethered deformation under an applied external mag-

netic ﬁeld. MSMs for active origami are obtainable by various

strategies, including embedding magnetic particles into a poly-

meric matrix or coating structures with magnetically responsive

metal particles.[182 ] The magnetic ﬁllers or coatings are the essen-

tial components of MSMs for generating mechanical load (body

torque) or heat under the external magnetic ﬁeld, realizing the

shape morphing of active origami. Various types of magnetic

ﬁllers, with ferromagnetic (soft-magnetic, hard-magnetic), or su-

perparamagnetic properties, behave diﬀerently under a magnetic

ﬁeld and require speciﬁc control strategies. Magnetic ﬁllers can

be integrated with inactive soft polymers or functional active ma-

trices of SMP, LCE, hydrogel, dynamic polymer, etc. Due to the

wide range of materials that MSMs can be based on, the stiﬀ-

ness and actuation stress of these materials varies accordingly.

In addition, MSMs can actuate rapidly, from tens of microsec-

onds to seconds.[37,38,276 ] This section focuses on how magnetic

ﬁllers and magnetic control facilitate reconﬁguration and loco-

motion of active origami systems. Active origami that incorpo-

rates magnetic ﬁllers with specialized polymeric matrices, for

example, inductive heating of SMP by embedding superpara-

magnetic particles, is discussed in the corresponding material

section.

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2.4.1. Magnetic Actuation Mechanism

The certain magnetic ﬁllers and coatings used in MSMs de-

cide their actuation mechanisms. Soft-magnetic materials (iron,

nickel, iron–nickel alloys) cannot retain strong remanent magne-

tization and can be easily de-magnetized and re-magnetized by

an applied magnetic ﬁeld. Because of this, these materials rely

on a gradient magnetic ﬁeld to generate force. Therefore, struc-

tures and materials embedded/coated with soft-magnetic mate-

rials require a gradient magnetic ﬁeld in order to be actuated. A

gradient magnetic ﬁeld can simply be obtained by a permanent

magnet.[277 ] A moving magnet can be used for locomotion and

navigation of MSM active origami systems due to the attraction

force toward the magnet. However, the magnetic ﬁeld gradient is

typically nonuniform around a magnet, making the programma-

bility and accurate control of soft-MSMs relatively limited. On

the other hand, hard-magnetic materials such as chromium diox-

ide (CrO2), neodymium–iron–boron (NdFeB), and hard ferrite

can retain strong remanent magnetization after being magne-

tized under a strong magnetic ﬁeld (1.5 to 2 T). When a uni-

form magnetic ﬁeld is applied, a torque can be generated to ro-

tate the magnetic materials so that their magnetization is aligned

with the applied magnetic ﬁeld. Since a uniform magnetic ﬁeld

can be generated by a pair of Helmholtz coils, the use of hard-

magnetic particles as ﬁllers is thus promising, as more accurate

programmability and control can be obtained. Therefore, this sec-

tion mainly discusses MSMs using hard-magnetic materials (re-

ferred to as hard-MSMs). It should be noted that hard-MSMs can

be re-magnetized by either heating them to above their Curie

temperature followed by applying a strong magnetic ﬁeld (1.5–2

T) or by directly applying a strong magnetic ﬁeld. As illustrated by

a beam with the programmed magnetization along its axial direc-

tion (Figure 6a), micro-torques are exerted on the hard-magnetic

particles when their magnetization is not aligned with the applied

magnetic ﬁeld B. These micro-torques are transmitted to the soft

matrix and lead to a bending deformation under an upward mag-

netic ﬁeld.[278 ] Another prominent feature of hard-MSMs is the

ﬂexibility to pattern magnetization distributions on demand, per-

mitting complex shape reconﬁguration of active origami. Kim

et al.[37] developed a DIW printing method of hard-MSMs, which

programs the magnetization along the ﬁlament printing direc-

tion (more details discussed in Section 3.2.1). This enabled the

fabrication of magnetically responsive origami, for example, the

Miura–ori pattern in Figure 1c as well as the hexapedal structure

with various magnetizations shown in Figure 6b, which realized

wirelessly controlled, fast and reversible contraction under an ap-

plied magnetic ﬁeld.

2.4.2. MSM Origami

Magnetic actuation has been demonstrated for eﬀective fold-

ing of origami structures on a variety of scales, based on dif-

ferent structural fabrication and magnetization strategies. The

patterned magnetization, the external magnetic ﬁeld, and the

structural design (panels and hinges) determine the origami fold-

ing. Cui et al.[184 ] encoded magnetization of microscale origami

structures by fabricating nanomagnet arrays on submicron pan-

els with electron beam lithography. As illustrated by the crane

microrobot in Figure 6c, the panels were assigned with dis-

tributed magnetizations and the ﬂat sheet reconﬁgured to a “ﬂap-

ping conﬁguration” under the applied magnetic ﬁeld. Note that

the designed nanomagnet array possessed anisotropic proper-

ties, enabling reprogrammable magnetization by a specially de-

signed sequence of magnetic ﬁelds for a “hovering” mode. The

re-programmability of magnetic materials allows for adaptable

shape changing and tunable properties even after material fabri-

cation and thus enhances the functionality of active origami for

applications such as soft robotics, metamaterials, and reconﬁg-

urable structures. Alapan et al.[189 ] developed a reprogrammable

metamaterial (Figure 6d) using a soft composite embedded with

CrO2particles, which have a relatively low Curie temperature of

118°C. Speciﬁc panels were selectively heated >150°C (using a

laser) while a moderate 15 mT encoding magnetic ﬁeld was ap-

plied, which reprogrammed the magnetization pattern and main-

tained 90% of the initial magnetization magnitude. Alternatively,

Song et al.[279 ] demonstrated reprogrammable origami sheets

by ﬁrst integrating NdFeB particles and phase change material

(oligomeric polyethylene glycol) into microspheres, and then em-

bedding the magnetic microspheres into the elastomeric matrix

as shown in Figure 6e. Upon heating, the phase change material

in the microspheres melted and the magnetized magnetic parti-

cles rotated based on the applied magnetic ﬁeld direction. After

cooling down, the phase change material solidiﬁed, locking the

alignment of magnetic particles and the corresponding magneti-

zation. Through this strategy, an origami sheet was demonstrated

with various transformations into desired shapes under magnetic

actuation (Figure 6e). Other reprogrammable MSMs with further

integrated functions are also available based on covalent adapt-

able networks due to the nature of the polymeric matrix, which

will be discussed in the next section.

Apart from shape morphing structures and metamaterials,

MSM origami systems are also widely used for soft robotics.

Gracias and collaborators[186] have done extensive work on un-

tethered origami microgrippers (Figure 6f). The microgrippers

with magnetic coating allowed for wirelessly controlled navi-

gation in complex environments such as the stomach and in-

testines. In addition, the reversible opening and closing abili-

ties of the microgrippers under diﬀerent stimuli including pH

change,[30] temperature,[161,280] chemicals,[186 ] etc., have been

demonstrated for functions of object grasping, cargo transporta-

tion, and biopsy. Inspired by jellyﬁsh, Ren et al.[183 ] demon-

strated a hard-MSM swimming robot with an engineered hinge

as shown in Figure 6g. By manipulating the applied magnetic

ﬁeld proﬁles, the swimming robot had diﬀerent swimming mo-

tion modes for multiple functionalities such as the mixing of

chemicals and transporting of objects. Recently, Wu et al.[185]

demonstrated a magnetic origami robotic arm that integrated

multimodal deformations of stretching, folding, omnidirectional

bending, and multi-axis twisting into one system as illustrated

in Figure 6h. By integrating the distributed magnetizations and

precise magnetic control into serially arranged Kresling origami,

the robotic arm illustrated sophisticated motions that mimic an

octopus arm. In addition, a small-scale origami crawler was also

realized by Ze at al.[75] via simultaneous contraction of four Kres-

ling units (Figure 6i). Here, the magnetic actuation separated

the power source and control system out of the robot, enabling

the miniaturization of the origami structure. The crawler was

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Figure 6. MSM actuation mechanisms, origami, and applications. a) Actuation mechanism of hard-MSMs. b) Patterned magnetization of hard-

ical Society). f) Untethered microgripper capable of navigation in complex environments and grasping of objects (Adapted with permission.[186]

AAAS).

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Figure 7. CAN mechanism and origami. a) Bond exchange reaction schematic and typical CAN properties of self-healing, plasticity, andreprogramming.

b) Elasticity and plasticity of an SMP with dynamic covalent bonds and reprogrammable permanent shapes. Adapted with permission.[292 ] Copyright

LCE with multi-shape memory capabilities controlled by light-activated bond exchange and heat for shape deformation (Adapted with permission.[169 ]

2021, Wiley).

explored for multiple functionalities such as movement in a con-

ﬁned space, drug storage, and drug release. An additional notable

work based on Kresling origami was a soft amphibious robot with

swimming, jumping, and cargo transportation functionalities.[31]

2.5. Covalent Adaptable Network (CAN) Polymers

Covalent adaptable network (CAN) polymers[281 ] are crosslinked

polymers with dynamic covalent bonds that can reversibly break

and re-form while maintaining network integrity (Figure 7a).

They are also often referred to as dynamic covalent polymer net-

works (DCPNs),[282 ] or vitrimers.[283 ] Under an applied stimu-

lus, often heat,[283–285 ] light,[286 ] or solvent,[287 ] the so-called bond

exchange reactions (BERs) become active in the network (see

Figure 7a, left), which lead to interesting merits such as plastic-

ity, recyclability, self-healing, and ease of reprogramming, equip-

ping CANs with specialized functionalities as compared to the

aforementioned materials (Figure 7a, right).[281,282] These have

led to applications such as healable sensors[288 ] and healable tri-

boelectric nanogenerators.[289 ] As we will discuss, dynamic cova-

lent chemistry (DCC) can be incorporated with active materials

to achieve active origami with outstanding properties.

2.5.1. CAN Mechanism

Typical CAN polymers involve BERs that enable the rearrange-

ment of networks. Common chemistries that possess BERs in-

clude transesteriﬁcation, disulﬁde exchange, imine exchange,

Diels–Alder (D–A), etc. Generally, the reactions that allow for

adaptability of bonds are dissociative or associative.[290 ] Dis-

sociative (such as D–A) networks involve covalent bonds that

are not necessarily re-formed upon breaking, allowing for sig-

niﬁcant decrease in the number of crosslinks in the net-

work. For associative (such as the abovementioned exchange

reactions except for D–A) networks, the overall number of

crosslinks in the network remains the same.[281 ] Upon acti-

vation of BERs, topological rearrangement of the network oc-

curs, where nearby bonds break and re-form, which can allow

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for plastic deformation of the material[282 ] and shape repro-

gramming. In addition, when BERs cross the interface be-

tween two CAN polymers, welding, reprocessing and recycling

are enabled. Figure 7b shows how BERs can be used together

with shape memory eﬀects to achieve diverse programmability

and shape change. The shape memory eﬀect allows the poly-

mer sheet to be programmed into a temporary shape and to

be elastically recovered to the permanent shape (Figure 7b-i)

while the permanent shape can be plastically reprogrammed by

BERs (Figure 7b-ii). Since the chemical reaction kinetics typically

follow Arrhenius law,[291] thermoresponsive BERs only become

fast enough (or active) to allow appreciable changes at high tem-

peratures (TBER). In addition, since BERs require macromolec-

ular chains to have enough mobility for exchange reactions, the

temperature for BERs to be active is typically higher than Tg.This

permits the possibility to combine the merits of BERs with shape

memory eﬀects.

2.5.2. CAN Origami

Xie and coworkers have pioneered multiple notable works on

CANs paired with SMPs to create active origami. In their ini-

tial works,[292,293 ] they achieved elasticity and plasticity within the

same polymer network. Plasticity could be induced by transes-

teriﬁcation BERs, allowing for reprogramming of complex 3D

permanent shapes upon heating to TBER. By deforming the sheet

while above its Ttrans (but below TBER) followed by cooling, tem-

porary origami shapes could be imparted (Figure 7b-iii). Upon

heating, the original origami shape would be recovered. By rais-

ing the temperature close to or above TBER, the permanent shape

could be reprogrammed. In a later work, they again used plas-

ticity and elasticity concepts, but to demonstrate the ability of

2D origami substrates to transform to 3D origami[294 ] via plastic-

ity, while reversible elastic deformation could occur at this state,

showing value for deployable structures that require subsequent

localized actuation. Plasticity of SMP CAN origami has also been

explored by other groups recently.[295,296]

Pei et al. incorporated reversible links into LCEs to achieve

easy processing and alignment after the initial cross-linking, en-

abling reprogramming.[297 ] They later utilized this concept to

demonstrate CAN active origami.[298–302 ] Via transesteriﬁcation

reaction, they showed that light-activated CNT-dispersed LCE

could be aligned spatio-selectively, in which local parts of the

material could be photothermally heated until transesteriﬁcation

was activated, after which those parts of the LCE actuator could

be aligned via stretching.[299 ] They presented another approach

that used CANs for jigsaw-like assembly of multimaterial origami

substrates.[298 ] Three CANs with diﬀerent TBERswereusedto

weld the materials via hot press to ﬂat crosses of varying material

arrangement. Upon programming a box shape and subsequent

heating, un-folding of multimaterial boxes (Figure 7c) could oc-

cur in diﬀerent sequential orders due to the order in which the

material phase transitions occurred. They additionally demon-

strated LCE CANs activated by solvent,[301,302 ] allowing for actua-

tion of LCE origami, such as Miura–ori, 3D kirigami structures,

and ﬂower-like actuators at relatively moderate temperatures.

Bowman and coworkers have made signiﬁcant advance-

ments in the understanding of covalent adaptable networks[281 ]

and developed the ﬁrst known light-triggered bond exchange

reaction.[286 ] Unlike photothermal eﬀects, they used light to di-

rectly trigger bond exchange reaction (or reversible addition-

fragmentation chain transfer (RAFT)).[286 ] The light-triggered

BER was later used to demonstrate photo-origami[34] and has

demonstrated active origami with exciting properties.[169,303 ] De-

picted in Figure 7d, they developed LCEs which have light-

activated BERs that allowed for separate control of the LCE de-

formation and alignment.[169 ] Here, the RAFT functionality was

incorporated into the polymer backbone and enabled bond ex-

change of allyl sulﬁdes within the network. The light-induced

BER allowed for stabilized alignment of LCEs in a strained state,

resulting in stable, permanent origami shapes upon removal of

strain. When heated, these structures deformed to ﬂat sheets

and returned to the 3D shape upon cooling. In this way, re-

versible folding of Miura–ori was achieved. Additionally, they

demonstrated transformation between three distinct shapes, as

shown in Figure 7d, in which the 3D crane was the permanent

shape programmed via BER, the ﬂat crane was the isotropic

state, and a third temporary state was able to be temporarily

programmed via thermal quenching. Li et al. also demonstrated

triple shape memory of LCE boxes,[304,305 ] taking advantage of

both the glass and isotropic phase transition temperatures of the

LCE.

Active CAN LCE origami has also been demonstrated by Zhao

and coworkers,[170,306 ] who utilized anthracene moieties with liq-

uid crystals, achieving light-controlled cleavage (de-crosslinking)

and dimerization (crosslinking) under two UV lights of diﬀer-

ent wavelengths.170 In this way, de-crosslinked, inactive domains

could be introduced through the thickness of an LCE sheet,

which eﬀectively created a bilayer of the original LCE and the

newly de-crosslinked LCE. The de-crosslinked regions acted as

ﬂexible hinges and caused curvature of the sheet at ambient tem-

peratures, with the extent of bending controllable by the extent of

decrosslinking that was programmed through the thickness. Re-

gions with thicker inactive domains resulted in smaller bending

angles toward the de-crosslinked side. Upon heating the sheet,

contraction of the crosslinked regions led to an overall ﬂatten-

ing of the sheet and temporary loss of the origami shape. They

used the same sheet and progressively patterned more inactive

domains (See Figure 7e), to achieve origami shapes such as an

airplane, bull, and frog.

CANs were also recently demonstrated with MSMs. Kuang

et al.[307 ] introduced magnetic dynamic polymers by embedding

hard magnetic NdFeB particles in a D–A polymer matrix. At ele-

vated temperatures, cleavage of dynamic linkages was triggered,

allowing for reprogramming of the magnetization under rela-

tively low magnetic ﬁelds. They demonstrated this with a foldable

array of magnetic dynamic polymer squares, initially with hori-

zontal magnetizations opposite to those in neighboring columns

(see Figure 7f, left). This type of magnetization resulted in a

3D “W” shape upon an applied downward magnetic ﬁeld. With

the use of a photomask and IR light for photothermal heating,

the magnetizations of squares were selectively reprogrammed to

four diﬀerent diagonal magnetizations (Figure 7f, right). They

also demonstrated the use of simultaneous applied magnetic

ﬁeld and bond exchange to obtain stress-free bistable and mul-

tistable kirigami structures that would otherwise be diﬃcult to

fabricate without BER.

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Figure 8. Additional materials for active origami. a) Hydrophilic and hydrophobic graphene-based origami, which absorbs and desorbs water molecules

Although not thoroughly covered in this section, DCC can im-

part shape memory capabilities on hydrogels as well. Chen et al.

have recently developed ﬂuorescent hydrogel origami, which uti-

lizes dynamic covalent bonding to enable shape memory func-

tion of hydrogel and dual encryption applications. Messages pat-

terned on the hydrogel could be decrypted upon shape recovery

and UV light illumination.[308,309 ] Generally, CANs enable unique

properties of active origami that are otherwise diﬃcult to achieve

in SMPs, hydrogels, LCEs, or MSMs without DCC.

2.6. Other Materials

While numerous active origami works have been done with

SMPs, hydrogels, LCEs, and MSMs, there are additional stimuli-

responsive materials used for active origami worth highlighting

here. For simplicity, the materials discussed in this section are

categorized into the general groups of hygroscopic, thermore-

sponsive, and electroactive materials.

Hygroscopic materials are those that can absorb or desorb

water vapor and will thus change shape in response to varia-

tions in humidity. These materials are similar to hydrogels in

mechanism, however, unlike hydrogels, they do not require an

aqueous environment to operate. In an early study, Okuzaki

et al.[310 ] found that, for accordion-like origami actuators with

polypyrrole ﬁlms, sorption and desorption of vapor drastically

changed the elastic modulus of the polypyrrole material, result-

ing in reversible strains of nearly 150%. Other materials, such

as GO (graphene oxide), are hydrophilic and can adsorb water

molecules.[311 ] As seen in Figure 8a, Mu et al.[312 ] developed a

graphene-based “paper” that was composed of a hydrophobic

rGO (reduced graphene oxide) layer and a hydrophilic GO-

polydopamine (GO-PDA) layer. They fabricated a ﬂat cross

substrate with patterned GO-PDA hinges. Upon the photoin-

duced heat of NIR light irradiation, the GO-PDA regions released

water by desorption, causing a contraction of the layer and lead-

ing to upward bending of the rGO outer panels, which was

quickly recovered back to a ﬂat state by water adsorption upon

removal of the light. PDA along with PNIPAM have also been

functionalized as hinges on graphene origami substrates.[313 ] Cai

et al.[314 ] have demonstrated the humidity response of MXene

cellulose composites for actuation of bilayer origami structures

with polycarbonate membranes. Other membranes such as the

porous cationic poly(ionic liquid) demonstrated by Zhao et al.[315 ]

exhibited rapid folding and un-folding in response to humidity

changes in the presence of organic solvents such as acetone.

Another common material used for hygroscopic response

is poly(3,4-ethylenedioxythiophene) polystyrene sulfonate

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(PEDOT:PSS), a conductive polymer used for a myriad of elec-

tronic devices.[316 ] It has been used to create active origami

structures.[76,317 ] For example, Treml et al.[76] used PEDOT:PSS

as the active material for origami logic structures, in which

PEDOT:PSS was used with polypropylene to create humidity-

responsive waterbomb origami ﬁlms with bistability or multista-

bility (Figure 8b).

While thermal expansion mismatch in bilayer or multilayer

systems is often used to drive the shape change of active

origami, heat has been used in other ways to actuate origami.

For example, as temperature increases, polymers tend to soften,

which has been taken advantage of for origami structures, such

as the heating of polymer at pre-stressed metallic hinges of

microgrippers,[186,318 ] polymer sheets with reduced-thickness pat-

terned hinges and stretched rubber bands which actuate struc-

tures upon hinge softening,[319 ] as well as the folding of graphene

polyhedrons as a result of melting its polymer hinges.[320 ] In-

stances of the incorporation of graphene with bilayers in ac-

tive origami have been demonstrated.[321,322 ] For example, Tang

et al.[322 ] embedded thermally expanding microspheres (TEM)

into rGO/PDMS bilayers (Figure 8c). The microspheres, which

were heated via photothermal eﬀect by the rGO upon exposure

to light, were liquid hydrocarbons encapsulated by thermoplastic

shells. When heated, the shell softened and the hydrocarbon tran-

sitioned to a gas, enabling an expansion of the spheres which re-

mained after the outer shell hardened upon cooling. This expan-

sion of the rGO/TEM portion of the bilayer caused irreversible

bending toward the PDMS.

Shape memory alloys (SMAs) are an additional type of ther-

moresponsive materials that have been used often in active

origami applications.[323,324 ] As the name indicates, SMAs exhibit

a shape memory eﬀect similar to that of SMPs (but note that

SMAs had been used and developed prior to SMPs). In short,

these alloys can undergo a reversible phase transformation be-

tween martensite and austenite phases during which the crys-

tal structures change.[325 ] Due to their ability to recover their

shape even when under appreciable loads, SMAs have relatively

high actuation energy density as compared to other stimuli-

responsive materials and can be advantageous in this way. Note

that the allowable strain of SMAs varies by alloy, but is gener-

ally limited to <8%.[325,326 ] Diﬀerent SMA waterbomb-based de-

signs with reduced-thickness hinges have been used to demon-

strate biomedical stents capable of coupled radial and axial[12]

or circumferential[327 ] deployment. SMAs have also been used

for the deployment of waterbomb-based transformable wheels,

where SMA wire contracts radially when heated, allowing for

reconﬁguration of the wheels.[328 ] Additional works have used

SMA wires/springs as actuators for sunlight-adaptive Ron Resch

(Figure 8d)[17] or waterbomb[329 ] origami-based shading devices.

Additionally, SMA has been used toward robotics applications,

for instance the use of SMA wires for actuation of a peristaltic

origami crawler robot.[330 ] It should be noted that other impres-

sive examples of metal-based origami[331–333 ] include the surface

oxidation of platinum ﬁlms[334 ] and metallic bilayers.[335 ]

Dielectric materials are also used to create active origami,

or so-called electroactive origami. Common dielectric materials

involve ﬂuids, for example, dielectric liquid can be displaced

upon an applied voltage and subsequently drive the movement of

panels.[336,337 ] Figure 8e shows an example by Taghavi et al.,[336 ]

in which dielectric liquid was applied at the hinge of two op-

positely charged panels. Upon an applied voltage, the electro-

static attraction drew the panels closer to one another, resulting

in folding. With this concept, they demonstrated an accordion-

like artiﬁcial muscle and a ﬂapping origami crane. Dielectric elas-

tomers can reduce in thickness and increase in area when a volt-

age is applied to electrodes across the thickness direction[338 ] and

can be used for simple motions such as bending,[339–342 ] as well

as for more complex origami.[272,343–345 ] Recently, Sun et al.[346]

utilized origami systems with elastomer between carbon grease

electrodes. The initial 3D structures (via pre-stretching) were ac-

tuated by applying a voltage (enabling electrostatic force between

electrodes), which caused the dielectric elastomer to expand, un-

folding the structure. The applied voltage could selectively actuate

the hinges individually, enabling boxes and pyramids as well as

gripper functionality.

Lastly, ceramics are also suitable materials for active origami.

Several works have utilized inactive ceramics, such as elastomer-

derived ceramics[347,348 ] for origami demonstrations, while others

use active materials such as piezoelectric ceramics. Under an ap-

plied electric ﬁeld, piezoelectric ceramic materials such as PZT

(lead zirconate titanate) can expand in one direction.[349 ] By plac-

ing PZT between electrodes, voltage-driven actuation of the ce-

ramic can be achieved, which has been used for robotics[350–352 ]

and active origami applications.[23,353 ] Speciﬁcally, Suzuki and

Wood[23] have demonstrated the use of PZT as linear actuators

for an origami-inspired surgical robot.

3. Fabrication of Active Origami

As active origami involves the shape evolution of materials, the

fabrication and patterning of materials that facilitate complex de-

formations are of great importance. Here, we discuss the most

common methods used to fabricate active origami, including

molding and 3D/4D printing, as well as techniques used for mi-

cro and nano scale active origami. Table 2 provides a brief sum-

mary of the common fabrication methods.

3.1. Molding

Molding is a common method for fabrication of soft materials

in which precursor materials are poured into a mold and cured,

resulting in structures that take on the inner cavity of the mold.

Molding has been used in fabrication of SMPs, hydrogels, LCEs,

MSMs, and CANs. For SMPs, molding can initially be used to

obtain the “permanent” shape of the material, while additional

molds or methods for shape ﬁxation can be used to program tem-

porary shapes. Fabrication of hydrogel structures also commonly

utilizes molding,[148,154,354,355 ] where multi-step processes can be

used to create bilayers or in which photomasks are used to in-

troduce crosslinking densities. Molding of LCEs[168,169 ] has been

used to introduce origami patterns into LCE sheets. Intricate

molds with micro-scale features such as microchannels[269,271 ]

have been used, which leads to alignment of the mesogens along

the channels to produce ﬁlms with complex director ﬁelds. For

cured MSMs with hard-magnetic particles such as NdFeB, the

material can be placed in ﬁxtures which conﬁgure the material

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Table 2. Summary of fabrication methods.

Method Material properties Active materials used Pros Cons

Molding Photo or thermally curable SMPs, Hydrogels,

LCEs, MSMs

Inexpensive Low structural complexity;

requires mold for each

new design

Direct ink writing (DIW) Viscous ink, shear-thinning SMPs,

Hydrogels, LCEs,

MSMs

Inexpensive; more material

choices

Low resolution;

slow

Fused ﬁlament fabrication

(FFF)

Thermoplastic SMPs,

Hydrogels, MSMs

Inexpensive Low resolution;

slow

Digital light processing (DLP) Photocurable, liquid resin SMPs,

Hydrogels, LCEs,

MSMs

Fast (cures entire layer) Multimaterial printing

challenging

Two-photon polymerization

(TPP)

Photocurable via two-photon

absorption

Hydrogels, LCEs,

MSMs

High resolution Diﬃcult to scale up

Inkjet Photocurable liquid ink SMPs, Hydrogels Fast; high resolution;

multimaterial capability

Expensive; limited material

choice

to a desired actuation shape. The material can then be magne-

tized by applying a large magnetic ﬁeld, imparting a magnetiza-

tion distribution in the MSM[73,356,357 ] so that it would later conﬁg-

ure to that shape under an appropriate magnetic ﬁeld. It should

be noted that CANs can be fabricated in a similar way to that of

their matrix material, but with special considerations to the ma-

terial’s chemistry.

3.2. 3D/4D Printing

3D printing, or additive manufacturing (AM), has enabled the

rapid manufacture of custom designed parts. These techniques

have since been expanded to stimuli-responsive/shape-changing

materials to bring forth 4D printing,[358,359 ] or the printing of

structures whose shape, properties, or functions can evolve

over time. 4D printing has been widely adopted for the fab-

rication of complex, shape-evolving structures and materials.

Here, we will brieﬂy discuss the 3D/4D printing methods com-

monly used to fabricate active origami, including extrusion-based

printing such as direct ink writing and fused ﬁlament fabrica-

tion, the resin-vat based digital light processing, inkjet print-

ing, as well as two-photon polymerization for high-resolution

printing.

3.2.1. Extrusion-Based Printing

Extrusion-based printing includes direct ink writing (DIW) and

fused ﬁlament fabrication (FFF; often called fused deposition

modeling (FDM)). These two methods share many common fea-

tures, such as they both use nozzles to write lines to form layers

and eventually form 3D solids. Both methods have been popular

in the fabrication of active origami.

DIW deposits viscous liquid inks in the form of a line onto

a platform.[360 ] The rheological properties of the ink are of crit-

ical importance, as shear-thinning and rapid transition to dila-

tant behavior are needed for eﬃcient extrusion and subsequent

rapid shape-holding of the ink.[361 ] Because of this, rheological

modiﬁers, such as nanoclays, are often added to active mate-

rial inks, which can then be used to print origami structures

or hinges. The resolution depends on nozzle inner diameter

as well as the rheological properties of the ink. Since DIW uti-

lizes liquid resin, the deposited ink needs to be cured, either

directly after printing, or after the entire structure is printed.

Naﬁcy et al.[ 354 ] developed a DIW printing method for hydrogels

that exhibit complex deformation by creating bilayer structures

with two diﬀerent hydrogels, thermoresponsive pNIPAM and

thermally inactive poly(2-hydroxyethyl methacrylate) (pHEMA).

Using pHEMA as the base, active pNIPAM hinges were pat-

terned onto it, which were then surrounded by remaining inac-

tive material (Figure 9a-i). The folding box shown in Figure 9a-

ii experienced reversible folding and unfolding as the tempera-

ture changed below and above the pNIPAM’s LCST, respectively.

More complex deformation of hydrogel origami was demon-

strated by Gladman et al.,[362 ] who achieved biomimetic, plant-

like deformations of hydrogel bilayers upon immersion in wa-

ter. The ink used was mainly an acrylamide matrix embedded

with cellulose ﬁbrils, which were aligned along the printing di-

rection during extrusion (Figure 9b-i, enhanced swelling along

the ﬁlament direction) and allowed for anisotropic swelling. Af-

ter immersion in water and swelling of the bilayers, complex

curvatures of ﬂowers (Figure 9b-ii) were achieved, dictated by

the angles between the ﬁlaments of the bilayers. Aside from cel-

lulose, other materials such as nanomagnets have been used

in DIW printing of hydrogel. An acrylamide ink with NdFeB

magnets and nanoclay for shear-thinning was printed.[363] After

the matrix resin was cured, the magnetic hydrogel could be de-

formed and held in desired shapes for magnetization, imparting

a distributed magnetization within the material upon a large ap-

plied magnetic ﬁeld. With this technique, origami folding such

as Miura–ori, as well as box and ﬂower-like folding structures

were fabricated. Other works involving magnetic materials and

elastomers such as PDMS have demonstrated origami-like struc-

tures, such as a ﬂapping butterﬂy[364] under a gradient mag-

netic ﬁeld and reprogrammable movements of 3D magnetic soft

objects[365 ] via large impulse magnetic ﬁelds. First demonstrated

by Kim et al.,[37] DIW to program the magnetization of MSM inks

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Figure 9. Extrusion-based DIW and FFF for active origami structures. a) DIW of a hydrogel cross with thermoresponsive hydrogel hinges (Adapted with

reserved; exclusive licensee AAAS). e) Printing of LCE in 3D space onto supports which were then dissolved to result in a 3D LCE lattice (Adapted with

Royal Society of Chemistry). g) FFF of cylindrical MSM embedded in a silicone matrix for biomimetic motions (Adapted with permission.[382 ] Copyright

2020, Elsevier).

along the print direction[37,366,367 ] allows for materials with pre-

cisely deﬁned magnetization distributions (see also Figures 1c

and6b).Maetal.

[366 ] used this method in a multimaterial ap-

proach, such that MSMs and M-SMP were printed, enabling

metamaterials with segments of either M-SMP or MSM. The ob-

tained metamaterials had unique deformation modes, with the

MSMs deforming under magnetic ﬁelds and the M-SMPs requir-

ing heat for their deformation (Figure 9c). Other SMP origami via

DIW has been achieved, such as the work by Rodriguez et al.,[368 ]

which involved ink based on epoxidized soybean oil. With their

printing method, origami with initially ﬂat or 3D shapes could be

achieved.

DIW is also well-suited for printing of LCEs.[167,369–372 ] Due to

the shear forces experienced by the ink during extrusion through

the nozzle, mesogens in LCE ink can be aligned along the print

direction,[369,370 ] thus programming the material. Roach et al.[180]

demonstrated the use of a room temperature printable LCE ink

for its use in actuating the hinges of multimaterial structures.

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Wang et al.[373] tuned printing parameters to show the variable

actuation strain of LCE ﬁlaments in folding structures. By vary-

ing printing parameters such as the printing temperature, the

nematic order of the inner ﬁlament could be tuned. For exam-

ple, with high printing temperatures, the inner part of a ﬁlament

largely remained in a polydomain state (Figure 9d-i), which re-

sulted in reduced actuation strain of the material after curing.

Using this approach, they demonstrated controllable actuated 3D

states of a ﬂower-like substrate (Figure 9d-ii). DIW LCE printed

bilayers have also been demonstrated as hinges with controllable

fold angles[172 ] for robotics applications, as highlighted previously

in Figure 5h by Kotikian et al. Additionally, Peng et al.[179,374] have

developed fabrication strategies that combine DIW of LCEs with

other methods of 4D printing for multimaterial origami (as high-

lighted previously in Figure 5d). In a recent pioneering work, as

opposed to printing LCE onto a plate, they successfully extruded

LCE into 3D space, allowing for the creation of LCE-based struc-

tures that are not achievable by conventional DIW methods. As

shown in Figure 9e, by ﬁrst printing dissolvable (non-LCE) struc-

tural supports and then using the support as a starting point of

an LCE ﬁber, LCE ink was extruded and then stretched to gener-

ate ﬁbers in 3D space that maintained the ability of generating

high actuation strains. By printing numerous lines and then dis-

solving the structural supports, complex 3D LCE structures such

as the lattice pyramid in Figure 9e were achieved.

FFF (or FDM) involves the extrusion of melted thermoplas-

tic ﬁlaments, which experience solidiﬁcation after cooling. The

main diﬀerences between DIW and FFF lie in material types: FFF

predominately prints thermoplastics and DIW is mainly used for

network polymers. SMPs (such as polyurethane or polyethylene)

printed by FDM have been used for programming of temporary

shapes.[137,375–377 ] In addition, tuning of printing parameters can

be used to introduce the desired stress during the printing pro-

cess, which later can be employed for shape change.[378–380 ] van

Manen et al.[ 378 ] utilized the polymer chain alignment along the

direction of extrusion enabled by the stretching of the melted

thermoplastic materials through the nozzle. The stretched de-

formation was memorized into the material after the ﬁlaments

cooled below Ttrans. By stacking layers with diﬀerent print di-

rections (Figure 9f), deformations such as bending and twisting

were achievable, due to strain mismatch between layers upon

heating. Origami capable of water absorption has also been fab-

ricated by FFF. Baker et al.[381 ] printed hydrophilic polyurethane

sandwiched between two layers of hydrophobic polyurethane,

with gaps to create bilayer hinges than would bend when placed

in water. Lastly, FFF has also been used for magnetic material

origami,[382,383 ] in which FFF-printed magnetic components[382 ]

were oriented in a soft silicone matrix to program magnetiza-

tion and enable biomimetic motions (Figure 9g) as well as direct

printing of thermoplastic rubbers with incorporated soft mag-

netic particles.[383 ]

3.2.2. Digital Light Processing (DLP)

DLP is a vat-photopolymerization printing approach that involves

light projected onto a vat of photocurable resin, which cures

one layer of the resin at a time, after which the printing stage

is moved, allowing for subsequent layers of the desired struc-

ture to be printed. DLP is relatively fast, as an entire layer of

the resin can be cured at one time, with resolution possible at

tens of microns.[384,385 ] As DLP involves a vat of resin, it is often

challenging to achieve multimaterial printing, but Ge et al.[386 ]

addressed this by using an automated material exchange sys-

tem (Figure 10a), in which acrylate networks of diﬀerent com-

positions could be used to create SMP structures, for example a

ﬂower with petals of diﬀerent Ttrans. Multimaterial DLP has also

been achieved by use of multicomponent resins in which mate-

rials could be preferentially cured under diﬀerent wavelengths of

light, resulting in structures containing components of diﬀerent

stiﬀness and swelling behaviors.[387 ] While SMPs often need to

be mechanically programmed after printing,[129] other methods

have avoided this by introducing diﬀerential crosslinking along

the thickness direction[388 ] to cause bending. Zhao et al.[389 ] did

this by utilizing frontal photopolymerization to fabricate Miura–

ori, a crane, and a variety of polyhedron. In a later work,[390] they

used DLP to introduce out-of-plane crosslinking gradients into

a ﬂat ﬁlm, which, upon immersion in water, resulted in desol-

vation of uncured chains from the ﬁlm, inducing contraction to-

ward the side of the ﬁlm that was less cured. By creating ﬁlms

with fully cured panels and hinges that were diﬀerentially cross-

linked, origami structures were made which exhibited bending

at the hinges only (Figure 10b). The structures could be ﬂat-

tened again by immersing the substrate in acetone, during which

the less cured region swelled. Another similar approach involv-

ing volatilization with an added post-curing step enabled origami

with enhanced material stiﬀness and the ability to hold apprecia-

ble weight.[391 ]

Another method to introduce diﬀerent material properties

into the same network was achieved with the use of grayscale

light, such that light intensity varies within the projected light

pattern. With a two-stage curing approach, Kuang et al.[392] devel-

oped SMP structures with speciﬁc material properties imparted

both within the layers and throughout the part, involving, for

example, structures with materials of diﬀerent moduli and Ttrans.

As shown in Figure 10c, a long strip with hinges of diﬀerent

Ttrans allowed sequential folding of the SMP strip to a spiral

shape upon gradual heating. The advantage of this approach is

that it uses only one resin vat and retains DLP’s merits of high

speed and high resolution.

DLP has also been applied to LCEs with the assistance of post-

processing. Jin et al.[393 ] used a solvent-assisted programming ap-

proach. In their work, liquid crystalline organogels were used,

in which swollen and crosslinked 2D sheets or 3D LCE struc-

tures were deformed, followed by solvent evaporation in the de-

formed shape. The swelling of the organogels lead to ﬂexibility

of the LC alignment and, upon deformation and subsequent dry-

ing, a new alignment of the mesogens was obtained, with mi-

cropores formed during drying helping to memorize the pro-

grammed director. Upon heating, the structure returned to its

printed shape (Figure 10d). Hydrogel origami fabrication has

also beneﬁtted from DLP,[394–396 ] with a notable example from

Kim et al.,[394 ] in which biomimetic structures were achieved

with hydrogel bilayers made from silk ﬁbroin bio-ink. The bi-

layer consisted of a ﬂat layer and a patterned layer, where dif-

ferential swelling led to curling toward the patterned layer in

water. Structures such as a folding ﬂower and venus ﬂytrap

were demonstrated (Figure 10e). CANs have also been fabricated

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Figure 10. Digital light processing for fabrication of active origami. a) Multimaterial DLP of SMP origami structures (Reproduced with permissionf.[386]

the Authors, some rights reserved; exclusive licensee AAAS). d) Solvent-assisted programming and reprogramming of LCE structures (Adapted with

with DLP,[32,397,398 ] speciﬁcally, shape memory networks with self-

healing capability[398,399 ] and welding for modular assembly[32] of

origami structures. Although the use of photopolymerization via

DLP is typically not well-suited for the opacity of soft magnetic

materials, Xu et al.[192] utilized DLP to construct magnetic soft

robots with NdFeB particles that could be aligned to arbitrary 3D

magnetizations. Foldable structures such as an accordion sheet

and grippers (Figure 10f) were achieved, which could locomote

with cargo.

3.2.3. Inkjet Printing

Inkjet printing, which utilizes commercial printers such as

those from Stratasys, is a common method for the fabrica-

tion of multimaterial origami structures. Inkjet printers deposit

droplets of ink onto the printer bed, which is then smoothed

and photocured to produce layers of material (see Figure 11a).

Inkjet printers often have multiple printing heads, which en-

able printing with multiple materials, however, the materials

that can be used with inkjet printing are limited by those com-

mercially available, which are mainly SMP and hydrogels,[358]

along with the fact that these exact materials are not typi-

cally disclosed. Nevertheless, many origami works fabricated by

inkjet printing have been demonstrated, such as self-locking

(Figure 3e) or sequentially foldable (Figure 1c) boxes, Kresling-

based metamaterials (Figure 3h), pyramids (Figure 1c), ﬂow-

ers (Figure 3f), and planes (Figure 5e) as shown in previ-

ous ﬁgures.[35,71,117,127,135,204,400,401 ] Another example is shown in

Figure 11b, where elastomer and glassy polymers are printed

Figure 11. Inkjet printing for active origami fabrication. a) Schematic of an inkjet printing process with multiple materials (Adapted with permission.[403]

2018, Elsevier).

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Figure 12. Micrometer and nanometer-scale fabrication techniques for active origami. a) Micrometer-scale molds used to fabricate diﬀerent hydrogel

within the same rods to produce patterns that generate dif-

ferent types of deformation upon heating.[402 ] Notably, inkjet

printing has enabled the printing of “digital” materials,[117,358,400 ]

which combine diﬀerent ratios of base printing materials for

origami structures with diﬀerent material properties and folding

capabilities.

3.3. Micro/Nano Scale Fabrication

As active origami shows great potential for applications in

biomedical environments as well as foldable electronic devices

such as microelectromechanical (MEMS) and nanoelectrome-

chanical systems (NEMS),[53] methods that can be used to

fabricate origami structures at the micrometer and nanome-

ter scale are very important.[404 ] There have been numer-

ous examples of micro and nano-scale origami largely com-

posed of metal.[334,405–408 ] The demonstrated methods to fold

these structures include surface tension of molten solder at

hinges[405,406 ] and chemical reactions.[334,407 ] However, these

methods are often not applicable to soft active materials. One

approach taken by Guan et al.[355] to achieve microscale fab-

rication of soft materials was the use of molds with microw-

ells to create bilayer hydrogel structures that bend in water

(Figure 12a).

4D printing at the nanoscale is also possible through di-

rect laser writing (DLW), which utilizes two-photon polymeriza-

tion (TPP) to fabricate structures at a resolution of as high as

100 nm.[6] Via TPP, a laser initiates two-photon absorption and

subsequent two-photon polymerization. The material near the

pulse of the laser polymerizes while the rest does not, with the

extent of polymerization depending on the power of the laser and

duration of pulse. Thus, high-resolution heterogeneous struc-

tures can be obtained. TPP has been used for fabrication of fold-

able voxelated LCE,[409,410 ] swellable materials,[155,411 ] and mag-

netic materials.[412 ] As shown in Figure 12b, Jin et al.[155 ] uti-

lized TPP for the tuned polymerization of voxels in a hydrogel

structure. By scanning the laser in the hydrogel precursor and

varying the laser power, voxels with diﬀerent crosslinking den-

sity throughout the printed structure could be obtained. A pH-

responsive hydrogel umbrella structure with interspersed bilay-

ers was printed. Upon a change in pH, the hydrogel rim bi-

layer connected to the umbrella ribs would bend, causing rotation

of the ribs in a lever-like folding process. Tissue-like materials

can also be printed, as demonstrated by Villar et al.,[413] through

utilization of printed layers of droplets with diﬀerent osmolari-

ties connected by lipid bilayers. When water ﬂowed through the

bilayer, it caused the droplets to either swell or shrink, result-

ing in bending of the microscale structures toward the layer of

the initially more dilute droplets (Figure 12c). Aside from TPP,

other methods used in fabrication of active origami at microm-

eter and nanometer scales include photolithography[186,407,414,415 ]

and electron-beam lithography,[184,406] which use either light or

electron beams to pattern small features in the surface of a ma-

terial.

4. Origami Modeling

4.1. Modeling of Origami Structures

Structural modeling of origami enables the prediction of diﬀer-

ent mechanisms’ deformations (single degree of freedom or mul-

tiple degrees of freedom) and mechanical behaviors (stiﬀness,

foldability, and stability). Under the guidance of structural mod-

eling, appropriately designed origami mechanisms permit pre-

ferred deformations and functions under mechanical loads or ex-

ternal stimuli. Various structural modeling approaches have been

developed by using bar and hinge models, shell-element-based

FEA models, and solid-element-based FEA models (Figure 13).

The bar and hinge model[416 ] is a simpliﬁed representation

of an origami structure that substitutes the creases between

panels with connected bars (green lines), and extra bars can

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Figure 13. Strategies for structural modeling of origami. a) Bar and hinge models of both conventional origami patterns (left, adapted with

2019, National Academy of Sciences).

be added across the origami panel (blue line) to accommo-

date for the in-plane stiﬀness (stretching and shearing), as il-

lustrated in the left of Figure 13a.[417] Torsional hinge springs

are placed along the bars between panels and along the bars

across panels to model origami hinge folding and out-of-plane

panel bending, respectively. Various types of bar and hinge

models with one,[3,68,416,417 ] two,[418 ] or four[ 419] bars across the

panel have been developed. These structural modeling meth-

ods were applied to predict both linear and nonlinear responses

of traditional origami patterns (Figure 13a, left),[417] curved-

creased origami (Figure 13a, right),[420] as well as origami struc-

tures accounting for compliant hinges with a ﬁnite width be-

tween the panels (Figure 13b)[421] and active hinges with stimuli-

responsive actuations.[422 ] Based on the bar and hinge mod-

els, software such as Origami Simulator,[423 ] MERLIN2,[424 ]

and Tessellatica[425 ] have been developed for origami structural

modeling.

Although the bar and hinge models help reduce the cost of cal-

culations, it leaves out valuable information such as stress and

strain distributions in the origami structure during the folding

process. FEA is a widely used simulation method based on phys-

ical modeling, providing a higher accuracy compared to the bar

and hinge model. The shell-element-based FEA model is straight-

forward to adopt, as the thickness of origami panels is gener-

ally much smaller than the in-plane dimension.[61,64,98,127 ] The

shell-element-based origami panels consider not only in-plane

stretching and shearing, but out-of-plane bending as well. To

account for the rotation of panels about the hinges, both ideal

rotational spring hinges with zero width (Figure 13c)[64] and com-

pliant hinges with ﬁnite width (Figure 13d, left[426] and right[ 427 ])

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have been used, which are capable of capturing highly nonlinear

mechanical responses such as snap-through deformations.[64,427 ]

FEA simulations of origami structures based on 3D solid ele-

ments consider the ﬁnite thickness of origami panels and hinges.

Although this simulation technique is more computationally ex-

pensive than the others, the 3D modeling can take into account

the complex geometry of origami, for example, layered origami

structures composed of active and inactive materials, and thus

provides the most information for the origami folding process.

In addition, other physical information such as temperature gra-

dient, swelling due to water absorption, etc. can be incorpo-

rated. Considering the actual hinge width and thickness in the

3D models, diﬀerent methods have been adopted to ensure that

the folding of panels happens at preferred positions, namely at

the compliant hinges (Figure 13e–h).[71,75,125,135,428] Reduction in

hinge thickness (Figure 13e)[428] or introduction of cuts at hinges

(Figure 13f)[75] are generally used to generate compliant hinges

in structures based on a single material.[307,429 ] When multima-

terial fabrication is allowed, reduction in the material stiﬀness

(Figure 13g, top[71] and bottom[135 ] ) at hinges is an alternative

option to reduce the eﬀective hinge stiﬀness. As discussed be-

fore, layered structures combining active materials and inactive

materials are commonly used for shape reconﬁguration of ac-

tive origami. Correspondingly, 3D FEA models with multilayer

structures (Figure 13h)[125] are also widely seen in diﬀerent works

for the prediction of active origami actuation.[30,101,135,138,161,430 ]

It should be noted that the dynamics of actuation become im-

portant to the folding behaviors of origami structures, especially

for soft materials which can exhibit instabilities when actuated

rapidly.

4.2. Modeling of Active Materials

Active origami modeling inevitably requires modeling of the me-

chanical deformation and stresses of constituent active materials

in response to external stimuli. Depending on the material type,

the mechanical behaviors are coupled with certain physical ﬁelds.

Continuum mechanics-based constitutive models typically give

the equations describing how state functions, such as internal

energy, entropy, and stress, depend on state variables such as de-

formation gradient (or strain) and temperature, and sometimes

on internal variables speciﬁc to each physical ﬁeld. Incorporation

of constitutive models with numerical simulation tools, such as

FEA, enables the simulation of active response of materials and

origami under mechanical and multiphysical stimuli.

Active materials used in origami are often based on polymeric

materials, which exhibit large deformations. In this case, the

multiphysics behaviors (or constitutive behaviors) are generally

described by ﬁrst specifying the Helmholtz free energy as a func-

tion of macroscopic deformation and internal variables associ-

ated with the coupled physical ﬁelds.[431 ] The stress–strain rela-

tionship can then be given by taking the derivative of the free

energy with respect to the deformation. For instance, the Cauchy

stress 𝝈is given by:

𝝈=J−1𝜕ﬁ

𝜕FFT(1)

where Ψis the Helmholtz free energy density, Fis the deforma-

tion gradient, the superscript “T” represents the transpose, and J

=det(F) is the volume change. For a purely elastic network, the

free energy, denoted by Ψstretch, recovers the strain energy, which

depends on the conﬁgurational entropy due to network stretch-

ing only. Some speciﬁc forms of Ψstretch are available, such as neo-

Hookean,[432 ] Arruda–Boyce,[433 ] Ogden,[434 ] etc. Note that, in ad-

dition to Equation 1, certain equations that constrain other state

or internal variables may need to be satisﬁed due to the laws of

thermodynamics. A summary of the modeling of diﬀerent active

materials is given in Table 3.

4.2.1. SMPs

A large number of models have been developed for SMPs, as

summarized in the literature.[196,471 ] These models can be divided

into two classes: thermoviscoelastic models[197,435,436,439,440,443 ]

and phase evolution models.[437,438,441,442 ] The thermoviscoelas-

tic model has been widely used for amorphous polymers, in

which the shape memory eﬀects are due to the change in chain

mobility during glass transition. Based on this mechanism, the

general idea is to adopt the temperature-dependent viscosity in

the framework of viscoelasticity, thus leading to the term “ther-

moviscoelasticity”. For example, assuming the relaxation time

to follow the time-temperature superposition principle (TTSP)

in simple viscoelastic models, the shape memory eﬀects can be

captured.[436,443 ] Multibranch viscoelastic models are often used

to accommodate multiple relaxation modes in real polymers. In-

tegration of TTSP with multibranch models showed improved

capability in predicting the shape memory behaviors[197,435,440 ] or

capturing multi-shape memory eﬀects.[439 ]

The phase evolution model captures the physics in semi-

crystalline polymers, although it is also used to model amorphous

SMPs, in a so-called phenomenological manner. In the phase

evolution model, the material is continuously crystallized in a

loading process and the newly formed polymer crystals are as-

sumed stress-free. Crystals formed at diﬀerent instants can be

seen as diﬀerent phases, which undergo diﬀerent deformation

histories and thus carry diﬀerent free energies. With this concept

as the foundation, the Helmholtz free energy density function

can be expressed as:[464 ]

Ψ=CORΨstretch Fe

0→t+∫t

Δ(𝜏,t

)Ψstretch Fe

𝜏→td𝜏(2)

where COR and Δ(𝜏,t)d𝜏are the fractions of the originally ex-

isted phases and the later formed phases, respectively, Feis the

mechanical deformation gradient for diﬀerent phases with the

subscript t1→t2(or 0→t) denoting the deformation from time t1

to t2(or 0 to t), and Ψstretch is the free energy function due to net-

work stretching. Note that COR and Δ(𝜏,t) evolve based on certain

kinetic laws[441 ] to capture the shape memory behaviors. All the

evolving fractions in Equation 2 need to be tracked in numerical

simulations, which is computationally expensive. The eﬀective

phase model has been developed to address this issue.[472 ] In ad-

dition, the concept of phase evolution has been used not only in

the shape memory eﬀects of semi-crystalline polymers but also

in the shape memory or viscoelastic behavior of many active poly-

mers, such as CANs. This will be discussed more in Section 4.2.5.

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Table 3. Summary of modeling of active materials.

Material Additional terms in free energy State variables and internal variables

SMPs[197,435–443 ] Deformations;

phase fractions;

temperature; light; moisture

Hydrogels[444–449 ] Free energy due to substance mixing Deformations;

chemical species;

temperature

LCEs[252,450–457 ] Nematic free energy Deformations;

mesogen orientations;temperature; light

MSMs[356,458–463 ] Magnetic potential Deformations;

magnetic ﬁeld; magnetization density

CANs[464–470 ] Deformations;

phase fractions;

temperature; light; moisture

4.2.2. Hydrogels

Hydrogels can exhibit reversible volumetric changes by absorb-

ing or repelling water (or solvent). Thermodynamics and me-

chanics theories have been developed to capture the physical cou-

pling between the stretching of the network, mixing of the solvent

and the polymer, and network swelling.[444,446,447] In the pioneer-

ingworkbyHongetal.,

[444 ] the Helmholtz free energy density

was expressed in two parts,

Ψ=Ψ

stretch +Ψ

mix (3)

where Ψstretch and Ψmix represent the free energy due to the

stretching and the mixing, respectively. A commonly usedΨstretch

based on the Gaussian chain distribution is:[473 ]

Ψstretch =1

2NkT trace FTF−3−2lnJ(4)

where Nis the number of crosslinks per unit reference volume,

kis Boltzmann constant, and Tis the temperature. Note that

Equation 4 is slightly diﬀerent from the neo-Hookean form. Non-

Gaussian statistics-based forms of Ψstretch have also been used to

account for the limited extensibility of polymer chains.[447,448 ] The

free energy Ψmix due to the mixing of polymer and the solvent is

written based on the Flory–Huggins model:[474,475]

Ψmix =kTC ln vC

1+vC +𝜒

1+vC (5)

where vis the volume of a ﬂuid molecule, Cis the number of ﬂuid

molecules per unit reference volume, and 𝜒is the Flory–Huggins

interaction parameter characterizing the disaﬃnity between the

polymer and the ﬂuid.

With the above free energy form, Hong et al.[444] derived the

constitutive relations for the stress, chemical potential and ﬂuid

ﬂux under isothermal conditions. Later, Chester et al.[447,448] and

Duda et al.[446 ] developed general, continuum-mechanics frame-

works that could describe behaviors under complex thermo-

chemo-mechanical loadings. The temperature-dependent 𝜒(T)

has also been used to model hydrogels with temperature-driven

swelling/deswelling properties, such as pNIPAM.[448,449 ]

Implementation of the constitutive relations of hydrogels into

FEA codes enables the direct simulation of hydrogels with com-

plex geometry and under complex loadings.[448,476,477 ] For imple-

mentations in the FEA package ABAQUS (Dassault Systèmes,

France), the user hyperelastic material (UHYPER)[476] or user el-

ement (UEL)[248,252,478 ] the mesogens may be reoriented and LCE

may experience a phase transition between an ordered (nematic)

and disordered (isotropic) state. To describe the intrinsic cou-

pling between the deformation, reorientation of nematic order

and other stimuli ﬁelds, many constitutive models have been

developed.[252,450–453 ] Generally, the Helmholtz free energy den-

sity can be expressed as:[452 ]

Ψ=Ψ

stretch +Ψ

nematic (6)

where Ψstretch is the free energy due to network stretching

and Ψnematic is the nematic free energy.[248,452] The Ψstretch form

ﬁrst given by Bladon et al.[479 ] takes the energy form of neo-

Hookean but is measured between the supposed isotropic phase

and the current conﬁguration, which has been widely used in

literature.[450–454 ] The Ψnematic can be written as a function of

the nematic order, and various forms have been used.[450,452,480]

For polydomain LCEs, the free energy should take diﬀerent

forms in diﬀerent nematic regions.[451,453 ] In general, the to-

tal free energy is a function of the network stretching, pre-

ferred orientation, and the nematic order. Recently, constitutive

models have been developed for heat-[452 ] or light-responsive[455]

LCEs, as well as LCEs with internal dissipations.[456,457 ] In

addition, in many applications, the anisotropic thermal ex-

pansion of LCE with experimentally measured coeﬃcients

has been widely used in FEA to mimic the actuation of

LCEs.[179,208,373 ]

4.2.3. MSMs

MSMs can be classiﬁed into soft-magnetic and hard-magnetic

materials depending on the coercivity of the embedded mag-

netic particles. Many constitutive models on soft-magnetic elas-

tomers have been developed.[481–483 ] However, here the hard-

MSMs which are capable of complex active shape changes

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will be focused on. Zhao et al.[458 ] developed the ﬁrst gen-

eral continuum framework for 3D ﬁnite deformation of hard-

MSMs, in which the Helmholtz free energy density consists of

two parts:

Ψ=Ψ

stretch +Ψ

magnetic (7)

where Ψstretch represents the free energy due to the stretching of

the soft matrix and the magnetic-related free energy Ψmagnetic can

be expressed as the magnetic potential of the embedded hard-

magnetic particles, that is,

Ψmagnetic =−FM ⋅Bapplied (8)

where Mis the referential magnetization density and Bapplied is

the applied magnetic ﬁeld. Note that with the above Helmholtz

free energy, Zhao et al.[458] derived the constitutive relation for

the stress of hard-MSMs, which has been implemented into

ABAQUS through the user element (UEL) subroutine. Since the

work of Zhao et al.,[458 ] many reduced-order models for hard-

MSMs have also been developed to enable computationally low-

cost simulations and designs.[460–462,484,485 ]

4.2.4. CANs

Modeling macroscopic behaviors of CANs generally requires in-

corporating the molecular-level kinetics of chemical reactions

into the framework of continuum-level constitutive theory. Ac-

cording to how they are coupled, three main types of models

which utilize diﬀerent strategies have been developed. The ﬁrst

model is based on the concept of phase evolution. Long et al.[466 ]

developed the ﬁrst constitutive model for a light-activated asso-

ciative CAN network based on this concept. Since then, the same

concept has been applied to CAN systems with various types

of stimuli and dynamic bonds.[464–466,472,486 ] Here, the phase is

a more general representation of a small collection of polymer

chains. Upon external stimuli, the polymer chains can contin-

uously evolve due to the bond cleavage/re-formation. Using a

similar concept for the crystallization, here the newly reformed

chains are assumed stress-free. Therefore, the Helmholtz free

energy density can be given by Equation 2.[464 ] Kinetic laws

for the phase evolution are governed by the kinetics of chem-

ical reactions and thus coupled to certain stimulus ﬁelds (e.g.,

temperature, light, and chemical species). The phase evolution

model has been integrated with FEA, enabling predictive sim-

ulations of viscoelastic behaviors of CANs with complex 3D

geometries.[487–490 ]

The second model was developed by Vernerey et al.,[468,469] who

expressed the total free energy density in terms of a statistical

distribution of the chain end-to-end vector r, that is,

Ψ=∫Ω

𝜙(r,t

)𝜓C(r)dΩ(9)

where ϕis the end-to-end vector distribution, 𝜓Cis the free en-

ergy density of the single chain, dΩ=r2sin𝜃d𝜃d𝜔is a small vol-

ume element of the conformation space Ω. Note that ϕ(r,t)de-

scribes the density of chains whose ris within the element dΩ.

Upon deformation and chemical reactions, the distribution func-

tion is evolved following certain kinetic laws associated with the

reaction kinetics, which can capture the macroscopic CAN behav-

iors.

The above two models physically incorporate the molecular-

level reaction kinetics, as discussed in two recent reviews.[491,492 ]

In addition, the third type of approach incorporates eﬀects of dy-

namic reactions into phenomenological viscoelastic or viscoplas-

tic frameworks.[470,493 ] Thegeneralideaistousearheological

model with certain combinations of springs and dashpots to de-

scribe the CAN behavior. The viscous ﬂow behavior of diﬀerent

dashpots can be chosen to depend on diﬀerent stimuli follow-

ing the reaction kinetics or the TTSP to capture complex multi-

physics behaviors.

5. Conclusion

Active origami structures are appealing for many applications

in reconﬁgurable devices, robotics, biomimetic actuators, meta-

materials, aerospace, and biomedical environments and have

seen rapid development in recent years. In this review, we

have discussed common active materials and their actuation

mechanisms, along with applications of active origami, com-

mon origami fabrication techniques, and a brief overview of the

modeling of active materials and origami structures. Although

we have highlighted here the many exciting advances in the

ﬁeld of active origami, such as structures with reprogrammable

deformation, locomotive multifunctional origami robots, and

state-of-the-art fabrication techniques to enable self-folding,

we would like to point out the primary challenges currently

faced, as well as the pertinent opportunities related to active

origami.

While the low modulus of active polymers allows these ma-

terials to be applicable for several biomedical applications, soft

polymer-based structures also suﬀer from low actuation force

and poor mechanical strength, which is a signiﬁcant limitation

for many practical applications. Deeper exploration into spe-

cial design of origami hinges[493 ] as well as further develop-

ment of composite active materials[205,494–496 ] or methods to store

elastic potential energy[215 ] may be able to help address these

limitations.

Within the realm of fabrication, multimaterial structures,

which can be used in multi-stimuli response applications and

enable complex structures with distributed material rigidity, still

face limitations such as the compatibility of materials, as well

as printers capable of handling multiple diﬀerent materials or

even diﬀerent printing methods within one setup.[179,374 ] Devel-

opment of printers that could achieve this at a relatively low cost

remains a challenge. Additionally, while rapid 4D printing meth-

ods such as DLP have been well developed for SMPs, further de-

velopment of similar rapid 4D printing methods for materials

such as hydrogels, LCEs, and MSMs would be beneﬁcial. In ad-

dition to small-scale fabrication, the commercialization or wide-

scale production of these materials becomes important. Hydro-

gels have been commercialized for use in several everyday items

such as wound dressings and contact lenses[498 ] while CANs have

been used for material recycling and reprocessing. Certain kinds

of shape memory polymers are popular as heat shrink tubes or

shrinkable plastic sheets while Nitinol, a type of shape memory

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alloy, has been widely applied within biomedical, automotive,and

aerospace industries. For a material with complicated fabrication

such as LCE, however, industrialization may take considerably

longer.

In addition, the design of accurate, controllable folding mech-

anisms is of great importance for practical applications of

complex foldable structures. In terms of minimizing materials

and weight of a structure, a simpliﬁed actuator arrangement is

preferred that can still result in precise folding. The exploration

of instabilities[499 ] and buckling mechanisms to enable precise

folding and greater actuation force is suggested for deeper study,

to address the limitations currently seen in the folding of soft ma-

terials.

Important to the future of active origami are systems which

can eﬀectively integrate sensing capabilities for data acquisi-

tion in a variety of applications. While the ability to change

states in response to stimulus is inherent to the design of ac-

tive origami systems, those which can adapt to environments

and self-sense could result in nearly autonomous machines,

especially for robotics and soft actuator applications. As ac-

tive origami has enabled many biomimetic soft robotics ap-

plications, to further emulate these biological systems, more

sophisticated interactions between the soft robot and its en-

vironment are required. There have been recent works which

take advantage of active origami sensing,[73,220,500,501 ] however,

the demonstrated sensing capabilities are still rather undevel-

oped and should be studied further. Ideally, these origami sys-

tems would be tetherless or have on-board control systems ca-

pable of intaking sensory information from the surrounding

environment.

Overall, the ﬁeld of active origami has seen many exciting ad-

vancements in the past few years, which can be used toward

self-deployable and foldable structures on multiple size scales for

many aerospace, metamaterial, robotic, and biomedical applica-

tions. With the further development and exploration of structural

and material designs for active origami, unique solutions can be

reached for many engineering challenges seen in the abovemen-

tioned areas.

Acknowledgements

R.R.Z., S.L., and S.W. acknowledge support from the NSF Award CPS-

2201344 and the NSF Career Award CMMI-2145601. H.J.Q. and X.S. ac-

knowledge the support of an AFOSR grant (FA9550-20-1-0306; Dr. B.-L.

“Les” Lee, Program Manager).

Conﬂict of Interest

The authors declare no conﬂict of interest.

Keywords

active materials, folding, origami, origami modeling, stimuli-responsive

materials

Received: March 4, 2023

Revised: April 13, 2023

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Sophie Leanza is currently an undergraduate Chemical Engineering student at The Ohio State Univer-

sity and a research assistant for Stanford University.She will pursue a Ph.D. in Mechanical Engineering

at Stanford University following her undergraduate studies. Her research interests include stimuli-

responsive materials, soft robotics, and the shape morphing of structures.

2302066 (34 of 35)

www.advancedsciencenews.com www.advmat.de

Shuai Wu is currently a Ph.D. candidate in Mechanical Engineering at Stanford University. He received

his B.S. degree in Engineering Mechanics from Southwest Jiaotong University and M.S. degree in

Mechanical Engineering from University of California, San Diego. His research interests focus on

reconﬁgurable soft materials and structures and soft robotics.

Xiaohao Sun is a postdoctoral fellow in the School of Mechanical Engineering at Georgia Institute of

Technology.Prior to that, he was a postdoctoral associate in the Mechanical Engineering Department

at University of Colorado Boulder. He received his B.S. degree in theoretical and applied mechanics

from the University of Science and Technology of China in 2014, and Ph.D. degree in solid mechan-

ics from the same university in 2019. His research interests include mechanics of soft materials and

modeling and design for 4D printing.

H. Jerry Qi is a Professor of Mechanical Engineering at Georgia Institute of Technology and is the site

director of NSF Industry–University Cooperative Research Center on Science of Heterogeneous Ad-

ditive Printing of 3D Materials (SHAP3D). His research focuses on developing fundamental under-

standing of multi-ﬁeld properties of soft active materials, including shape memory polymers, light

activated polymers, liquid crystal elastomers, and vitrimers. He has been working on integrating active

materials with 3D printing and developing new materials and new methods in polymer 3D printing for

applications in morphing structures, metamaterials, origami, and soft robotics.

Ruike Renee Zhao is an Assistant Professor of Mechanical Engineering at Stanford University where

she directs the Soft Intelligent Materials Laboratory.Renee’s research concerns the development

of stimuli-responsive soft composites for multifunctional robotic systems with integrated shape-

changing, assembling, sensing, and navigation. By combining mechanics, polymer engineering, and

advanced material manufacturing techniques, the functional soft composites enable applications

in soft robotics, miniaturized biomedical devices, ﬂexible electronics, and deployable and morphing

structures.

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Hexagonal ring origami is a type of foldable structure that has impressive packing abilities and can be tessellated into two-dimensional or three-dimensional surfaces without any gap or overlap. It can be folded under bending or twisting loads into a peach core-shaped configuration with only 10.6% of its initial area. However, in applications of large-scale foldable structures, folding by bending or twisting is usually technically difficult. Here, we propose strategies to facilitate easy snap-folding of the hexagonal ring by a simple point load or localized twist or squeeze. This is enabled by two geometric modifications made to the hexagonal ring: introducing residual strain and creating pre-twisted edges. By combining theoretical modeling, finite element simulations, and experiments, we systematically investigate the snap-folding behaviors of modified hexagonal rings with residual strain and pre-twisted edges. It is found that the geometric modifications promote easy snap-folding of the hexagonal ring by different mechanisms: introducing residual strain can significantly decrease the energy barrier and thus reduce the required moment to snap-fold the ring, while creating pre-twisted edges allows for easy out-of-plane deformation which is a necessary condition for a ring to fold. Combining the two methods further enables the snap-folding of the hexagonal ring by a point load or localized twist or squeeze. To demonstrate the easy folding of large assemblies of the modified rings, we construct dome and pyramid assemblies that can be snap-folded from their initial three-dimensional states to significantly lower-volume final states by a simple compression at the rings’ corners. We envision that the proposed geometric modification strategies can provide a new perspective on the rational design of easy-to-fold ring origami-based foldable functional structures with extremely high packing ratios.

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Three-Dimensional Thermochromic LCE Structures with Reversible Shape-Morphing and Color-Changing Capabilities for Soft Robotics

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Functional structures with reversible shape-morphing and color-changing capabilities are promising for applications including soft robotics and biomimetic camouflage devices. Despite extensive studies, there are few reports on achieving both reversible shape-switching and color-changing capabilities within one structure. Here, we report a facile and versatile strategy to realize such capabilities via spatially programmed liquid crystal elastomer (LCE) structures incorporated with thermochromic dyes. By coupling the shape-changing behavior of LCEs resulting from the nematic-to-isotropic transition of liquid crystals with the color-changing thermochromic dyes, 3D thermochromic LCE structures change their shapes and colors simultaneously, which are controlled by the nematic-isotropic transition temperature of LCEs and the critical color-changing temperature of dyes, respectively. Demonstrations, including the simulated blooming process of a resembled flower, the camouflage behavior of a "butterfly"/"chameleon" robot in response to environmental changes, and the underwater camouflage of an "octopus" robot, highlight the reliability of this strategy. Furthermore, integrating micro-ferromagnetic particles into the "octopus" thermochromic LCE robot allows it to respond to thermal-magnetic dual stimuli for "adaptive" motion and diverse biomimetic motion modes, including swimming, rolling, rotating, and crawling, accompanied by color-changing behaviors for camouflage. The reversibly reconfigurable and color-changing thermochromic LCE structures are promising for applications including soft camouflage robots and multifunctional biomimetic devices.

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