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Schematic representation of (a) the RUC of a 2 Â 2 twill composite and its local coordinate system; (b) decomposition of the RUC into matrix, fill, and warp yarn plates assumed to be in parallel coupling. RUC: representative unit cell.
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An accurate prediction of the orthotropic elastic constants of woven composites from the constituent properties can be achieved if the representative unit cell is subdivided into a large number of finite elements. But this would be prohibitive for microplane analysis of structures consisting of many representative unit cells when material damage al...
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... one RUC, we introduce a local co-ordinate system such that coordinates 1 and 2 represent the fill and warp yarn directions, respectively. Then, the local direction 3 is the out-of-plane normal, as shown in Figure 1(a) for a twill 2 Â 2 woven composite. ...
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Citations
... While these micromechanics-based models are very effective, they can become computationally prohibitive for structural level analyses [25]. As a remedy to these issues, the recently developed microplanetriad model (MTM) has salient features that allow overcoming these issues to a large extent [31]. The model can capture mesoscale damage behaviors, predict lamina elastic constants as well as essential failure mechanisms, such as yarn tension fracture and matrix cracking. ...
... The microplane triad model (MTM) is a multiscale model capable of predicting the elastic and damage behavior of woven composite laminae, building up from the mesoscale properties of the constituents and the weave architecture [31]. The details of the model formulation, calibration, and composite coupon level validation has been presented previously in Refs. ...
... The details of the model formulation, calibration, and composite coupon level validation has been presented previously in Refs. [31] and [33]. It was shown in those references that the model is capable of predicting the complete stress strain curve and strength of various woven composite layups under tension, compression, and shear. ...
Existence of undulating fill and warp yarns in woven composite laminae introduces complex unit cell geometries and multi-scale interactions among the constituents. Due to these, the failure process involves various meso-scale constituent-level failure modes under complex loading scenarios such as ballistic impact, and can be challenging to model via conventional macro-scale damage tensor-based models. This challenge is tackled here via the adaptation of the previously developed multi-scale microplane triad model to ballistic impact of woven composites. The model can resolve meso-scale constituent level details (including yarn undulations) and predict not only the elastic constants of a woven lamina but also its fracturing behavior. In the present adaptation, only two damage laws are formulated, one for the fibers and one for the matrix. This enables the model to embody the correct values of the intralaminar mode I and II fracture energies of the woven lamina. The model is calibrated using constituent and lamina level test data, and then used to predict the ballistic impact behavior of a single plain-woven lamina under a wide range of projectile impact velocities. The model is demonstrated to predict very well the projectile residual (rebound and exit) velocities, the energy dissipation, the major failure modes of the lamina and the corresponding extent of damage, as well as the ballistic limit and deformation cone wave propagation speeds. The model’s simple, conceptually clear architecture, and computational efficiency represent a major advantage compared to existing damage tensor-based models. The model is also extended to multi-layer thick section woven laminate impact, where the analyses consider both intralaminar and interlaminar failures. The predictions are found to be comparable to those from MAT162, a commercially available material model in LS-Dyna, with much better computational efficiency. Via detailed sensitivity studies, it is revealed that the mode I and II intralaminar fracture energies of the lamina are a crucial model input, necessary for accurate predictions of ballistic impact. Not knowing these can introduce significant uncertainty and therefore, their characterization is an absolute must. Finally, the optimal meshing considerations as well as the advantages and limitations of the microplane triad model are discussed.
... In this section, the predictions of the proposed beam-spring model are first compared against available experimental data for plain-woven composites and also the results of some other theoretical models. It is worth mentioning that the undulation angle of yarns in these samples are relatively Elastic constant 29 24.80 ± 1.1 Scida at al. 29 23.50 Scida et al. 30 25.33 Barbero's PMM 31 25.10 Barbero's FE model 32 24.44 CLT 32 27.40 Kowalczyk 33 25.15 Triad microplane 34 27.71 This study 23.70 (|difference|= 4.4%) small (<5°), thus the softening effect of bending and shear deformations on the axial modulus is limited. ...
Engineering application of textile composites needs simple relations for the estimation of their mechanical properties. Many homogenization and simplified models have been already proposed for the analytical characterization of the elastic moduli of this class of materials. Along this route, the current study introduces an analytical solution for the longitudinal elastic modulus of plain-woven textile composites. A hybrid beam-spring model of the representative unit cell (RUC) is postulated consisting of a horizontal beam connected to an inclined beam, two supporting springs beneath the free end of the horizontal beam and the common end of the horizontal and inclined beams, and a torsion spring at the free end of the inclined beam. The mechanical and geometrical properties of the beams and springs are calculated from the weave structure and the symmetry conditions. A reduction technique from the matrix analysis of structures is borrowed to consider the effect of internal degrees of freedom on the in-plane stiffness coefficient and a closed-form formula is extracted for the elastic modulus. The proposed analytical formula is finally verified against available experimental data and a wide range of FE predictions for the GFRP and CFRP plain-woven composites.
... [12][13][14][15][16][17]. Polymers too exhibit failure via variety of damage mechanisms depending on the loading conditions, e.g., brittle fracture under tension but a combination of microplasticity, crazing as well as frictional slips under compression[2][18][19] ...
This paper presents a microplane constitutive model for the tensile and compressive damaging behavior of brittle-plastic glassy polymers. The model is formulated and validated using experimental data on such polymers and is an adaptation of the previous microplane model formulation developed for concrete. The model considers a material point as a Gaussian approximation of a unit sphere, discretized into several “microplanes”. The macroscopic strain tensor is projected onto these microplanes yielding various micro-strain vectors. The various damage mechanisms such as tensile microcracking, shear microplasticity, and micro-crack friction are formulated in terms of the microplane level strain vectors, yielding corresponding stress vectors. These are then homogenized via the principle of virtual work yielding the macroscopic stress tensor. One of the salient features of the present adaptation includes a volumetric-deviatoric (V-D) split in the microplane level stresses and strains. This enables properly capturing a Poisson’s ratio greater than 0.25, which happens to be the case with most polymers. On the other hand, a normal stress comparison algorithm is implemented to alleviate the overestimation of stresses which can happen due to the V-D split. The proposed adaptation is validated using experimental data from uniaxial tension and compression tests on two different polymers, which includes post-peak inelastic behaviors such as hardening and softening or both. The model shows excellent agreement with the experimental data, demonstrating its ability and applicability to accurately capture the various damage mechanisms in brittle-plastic glassy polymers. The results presented here are at the material point level, and the application to structure level problems via a user material subroutine in a finite element software is in progress.
... The constitutive equations of the matrix instead are modeled in each facet built inside the tetrahedral element. The tetrahedral mesh is constructed via Delaunay Triangulation, and it resembles the lattice discrete particle model proposed by Cusatis et al. [11][12][13][14][15][16][17]. The intricate material behavior of the matrix allows to capture the inherently complex damage mechanisms, both crack initiation and crack propagation. ...
This study focuses on the computational analysis of complex structural joints made of Carbon Fiber Reinforced Plastics (CFRP) manufactured via novel Additive Manufacturing (AM) techniques. The new discrete modeling framework DM4C (Discrete Model for Composites) is used, where fiber tows are modeled as Timoshenko beams and the resin as an ensemble of discrete facets anchored to a tetrahedral mesh. Firstly, the model parameters are calibrated to the macroscopic parameters of the chosen material system using a massively parallelized calibration technique coupled with Machine Learning and Artificial Intelligence (ML/AI) algorithms. Secondly, an advanced generalized generation algorithm is used to generate the complex joints which are then simulated. Finally, different joints are compared with each other. Preliminary results showed that truncating fibers always leads to lower structural strengths, highlighting the importance of optimizing fiber paths during manufacturing to reduce such fiber interruptions.
... As it will be shown in this presentation, in DM4C, fibers, bundles of fibers, and tows are simulated explicitly as Timoshenko beam elements while the matrix is described by vectorial constitutive laws defined on the facets of a tetrahedral mesh anchored to the nodes of the beam elements via a state-of-the-art highly parallelized laminate generation algorithm. These vectorial laws, which remind of the microplane formulation for quasibrittle materials [6][7][8][9][10][11][12][13], describe both the elastic and inelastic behavior of the matrix, including the traction-separation laws governing the fracture process and the friction between facets governing the compressive behavior. Thanks to the facet-based formulation, fracture is modeled in a discrete way and the need for element erosion can be avoided. ...
Unidirectional (UD) and 2D/3D textile composites are increasingly being employed in systems acrossed many industrial sectors including aerospace, automotive, and wind energy. This is due to the excellent specific mechanical properties and tailorability of composites, paving new avenues for structural optimization and weight savings. One of the challenges with the simulation of the mechanical response of composite materials is that their damage mechanisms depend strongly on the material micro-and mesostructures. Phenomena such as fiber micro-buckling and kinking in compression or fiber scissoring and matrix microcracking in shear in UD composites are only a few examples. Homogenized continuum models that describe these mechanisms are extremely mathematically complex, lack generality, and can only be used to fit experimental data. In fact, the constitutive equations compensate for not modeling fibers and matrix explicitly by introducing several complex equations and fitting parameters of unclear physical meaning. This makes model calibration extremely cumbersome and limits the predictive capability of the model. In reality, the modeling of damage and fracture in composite materials does not have to be complex if the physics of the micro-and mesostructures is simulated explicitly. This is the goal of the Discrete Model for Composites (DM4C), a novel discrete mesoscale modeling framework that simulates the mechanical behavior of UD and textile composites. Specifically, this framework is only based on physical laws and does not depend on element erosion to simulate fracture. As it will be shown in this presentation, in DM4C, fibers, groups of fibers, and tows are simulated explicitly as Timoshenko beam elements while the matrix is described by vectorial constitutive laws defined on the facets of a tetrahedral mesh anchored to the nodes of the beam elements. These vectorial laws describe both the elastic and inelastic behavior of the matrix, including the traction-separation laws governing the fracture process and the friction between facets governing the compressive behavior. Thanks to the facet-based formulation, fracture is modeled in a discrete way and the need for element erosion can be avoided. Furthermore, since fibers and matrix are now simulated explicitly, the constitutive laws of each material can be physics-based, simple, and with clearly defined material parameters. To demonstrate the predictive capability of the proposed framework, simulations of several typical damage mechanisms in composites will be compared to experimental data such as shear band formation in transverse compression, fiber micro-buckling and kinking in longitudinal compression, and sub-critical matrix microcraking in off-axis layers. _____________
... The constitutive laws for the matrix are defined on these facets resembling the lattice discrete particle model [18][19][20]. A simple and physics-based representation of a material is introduced in the vectorial form of constitutive relation comparable to the microplane formulation [21][22][23][24][25][26][27]. Furthermore, it reduces the number of curve-fitting parameters in calibration. ...
This study presents a numerical exploration of the effect of tow in-plane waviness on the mechanical behavior of 3D printed composites. A new, discrete modeling framework (DM4C) which models the printed fiber tows explicitly with Timoshenko beams is described and utilized for this effort. To evaluate the fracture toughness of the additive manufactured composite laminate, center cracked tensile specimens with four different laminate configurations are simulated: one cross-ply laminate and three laminates with varying amplitude in sinusoidal wavy reinforcement layers. The wavy laminate with the largest amplitude showed an increase in structural strength by 25 %. Interesting toughening mechanisms are observed in the wavy laminates.
... However, the wide applications of thermoplastic PPCs in the future inevitably require computational modeling to assist the design of their composite structures. Conversely, computational modeling just on the mechanical behavior of carbon-/glass-fiber-reinforced polymers at various length scales has been largely investigated in the literature (e.g., [390][391][392][393][394][395][396][397][398][399][400][401],etc.). ...
Thermoplastic polymer fiber-thermoplastic polymer matrix composites (PPCs) or polymer-fiber-reinforced polymers(PFRPs), often recognized as self-reinforced or single polymer composites, are potential candidates for future advanced polymer composites because of various advantages (e.g., recyclability, formability, low-cost, ultra-lightweight, environmental friendliness, etc.). The manufacturability and mechanical behavior of these composites compared to conventional carbon-/glass-/aramid-fiber-reinforced polymers is of great interest to the composites community, but there are a limited number of studies in this area.
To this end, this paper reviewed fabrication methods with different processing parameters and mechanical behavior of uni-/multi-directional thermoplastic PPCs featuring continuous thermoplastic polymer fibers from limited data in the literature. It was shown that most specific behaviors (normalized by density) of these materials in various loading conditions (e.g., quasi-static tension/shear/flexure, tension-tension fatigue, and out-of-plane impacting, etc.) are comparable to or better than glass-/aramid-fiber-reinforced polymers. Particularly, the specific ductility in the foregoing conditions outperforms all the carbon-/glass-/aramid-fiber-reinforced polymers. Thermoplastic PPCs with remarkable performance can be achieved through several uncomplicated methods (e.g., film stacking, hot compaction, powder and solution impregnations, matrix infusion and injection molding, additive manufacturing, etc.), which have some similarities to the methods used for carbon-/glass-/aramid-fiber-reinforced polymers. Moreover, several opportunities and challenging problems of thermoplastic PPCs were summarized at the end of this review paper. Efficient solutions may require countless efforts in the composites community to further strengthen the performance and understanding of thermoplastic PPCs for wide applications in various engineering fields in the future.
... The contribution of the N plane to the total stiffness tensor of the transversely isotropic UD lamina is denoted as ( ) and can be calculated as [19]: ...
... where the constants , , , , are related to the components of the fourth order elasticity tensor of the unidirectional lamina [13] [19]. On the other hand, the contribution of the cylindrical microplane stiffness is denoted as and is expressed as: ...
Prior studies have provided experimental evidence of the size effect on the nominal strength of fiber composites, failing by the formation of a kink band under compression. This size effect is analyzed here computationally with the goal to understand and quantify the role of crack face friction. The mechanism of kink band formation is modeled by the semi-multiscale cylindrical microplane model, recently calibrated and experimentally validated for its predictions of the failure geometry as well as strength size effect. The kink band initiation in the model is driven by damage triggered on cylindrical microplanes. The model embodies a combined damage friction formulation on the microplane level, which assumes a parallel coupling between the two mechanisms. The model is used here to predict the strength size effect with and without friction effects. In the friction-free models, the predicted strength is found to scale in accordance with linear elastic fracture mechanics, suggesting brittle fracture. On the other hand, in the models embodying friction, the fracture process zone size is found to be enlarged, and the predicted strengths are found to not only obey the Bažant size effect law, but also match the test data. The strengths are found to fall in the transitional portion, suggesting quasibrittle fracture. Thus, the inclusion of friction is found to considerably increase the degree of quasibrittleness, and the combined friction/damage based microplane model employed here, is found to be useful to quantify this increase.
... The microplane modeling approach has been widely used to capture such two-scale failure mechanisms in a variety of isotropic quasibrittle materials, such as concrete [62][63][64] and rocks [62]. The microplane approach has been adapted for anisotropic materials too, e.g. for shape memory alloys [65], the spectral stiffness microplane model for unidirectional and woven composites [66,67], the microplane triad model J. Xue and K. Kirane developed for woven composites in [68,69] and the spherocylindrical microplane model for shale [70], but not yet for kink band failures in composites. ...
... The broader framework for the present model is provided by the microplane triad model, which was developed recently in [68,69]. This is a semi-multi-scale model, able to accurately predict the elastic and tensile fracturing behavior of woven composites, via upscaling of the mesoscale elastic properties as well as the damage evolution. ...
... We denote the unit normal vectors for the three microplanes of a triad as , , and while the three shear or tangential vectors as , , and . Thus for a triad we have six microplane level strain vectors, denoted as , = , , , , , [68]. These strain vectors are obtained by the projection of the local strain tensor obtained from the global strain tensor as described in the previous section. ...
This two-part paper presents a novel 3D cylindrical microplane model for the longitudinal compressive failure of fiber reinforced composites by kink band formation. The formulation details are presented in part-I, while the implementation, calibration, and validation, in part-II. The primary novelty is the first adaptation of the semi-multiscale microplane modeling approach to compressive kink band failures in composites. The salient novel feature of this adaptation is a cylindrical system of microplanes, introduced to capture the transversely isotropic behavior of the unidirectional lamina. The model implicitly resolves the macro–micro compatibility to calculate the local fiber rotation in the kink band, thus defining the orientation of the cylindrical microplane system. This allows an intuitive formulation of the kink band triggering mechanism involving axial inter-fiber microcracks at the microplane level. As another new advance, the internal friction is formulated at the microplane level, via a thermodynamically consistent combined damage/friction scheme, which is integral to compressive failures. The model formulation is general enough to allow application to both brittle and ductile matrix materials, and to in-plane and out-of-plane kinking. The macro–micro elastic correlations are established via strain energy density equivalence, and the calculation of the stiffness tensor of one microplane system is demonstrated.
... Young's modulus, Poisson's ratio, and shear modulus respectively of uncracked concrete (9), (21), (24) fc, fr Uniaxial compressive strength and uniaxial tensile strength respectively (6), (9) εo, εr ...
Emerging 3D printed concrete techniques has raised numerous possibilities in contemporary architectural creations that are often beyond the scope of prevailing structural design standards. Rigorous, three-dimensional, and nonlinear finite element analysis (NLFEA) with appropriate constitutive modelling of materials would be inevitable when analysing complex structures. However, many existing concrete models could hardly handle those structures' complicated behaviour, including crack-induced anisotropy, changeable stress transfer mechanisms, shear-slip and re-contact, mesh-size sensitivity, etc. Hence, this paper has developed a novel and experimentally validated constitutive model to tackle the above issues. The novel features include (1) highly robust total-strain formulation, (2) cyclic normal and tangential stress-strain responses, (3) a novel algorithm for uniquely fixing the 3D crack plane coordinate, (4) the equivalent strain transformation for modelling the axial-lateral strain interaction, (5) shear-slip and re-contact behaviour of cracks, and (6) mesh-size sensitivity mitigation. The proposed model was implemented into ABAQUS's user-subroutine and applied to simulate a full-scale column test with specimen height = 5 m. The tested column, subjected to a constant vertical load and a cyclic load in the horizontal direction, failed in shear. The simulation can capture the damage evolutions and hysteresis response of the tested column. Hence, the proposed modelling framework could serve as a basis for analysing and designing concrete structures with unconventional shapes under non-proportional loading.
