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Published in Journal of Rehabilitation Research and Development 41(6A):pp. 775-786.
Copyright 2004 US Department of Veterans Affairs
FINITE ELEMENT ANALYSIS TO DETERMINE THE EFFECT OF MONOLIMB FLEXIBILITY
ON STRUCTURAL STRENGTH AND INTERACTION BETWEEN RESIDUAL LIMB AND
PROSTHETIC SOCKET
Winson C.C.Leea, BSc; Ming Zhanga,*, PhD; David A. Boonea, CP, BS, MPH; Bill Contoyannisb
a Jockey Club Rehabilitation Engineering Centre,
The Hong Kong Polytechnic University, Hong Kong, China
b REHABTech, Monash University, Melbourne, Australia
* Correspondence address:
Ming Zhang (PhD)
Jockey Club Rehabilitation Engineering Centre,
The Hong Kong Polytechnic University,
Hong Kong,
P.R. China.
Tel: 852-27664939
Fax: 852-23624365
Email: rcmzhang@polyu.edu.hk
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ABSTRACT
Monolimb refers to a kind of transtibial prostheses having the socket and shank molded into one
piece of thermoplastic material. It has a characteristic that the shank made of such a material can
deform during walking which can simulate the ankle joint motions to some extent. The changes of
the shank geometry can alter the stress distribution within the monolimb and at the residual limb-
socket interface, and respectively affect the deformability and structural integrity of the prosthesis
and comfort perceived by amputees. This paper described the development of a finite element model
for the study of the structural behavior of monolimbs with different shank designs and the interaction
between the limb and socket during walking. The von Mises stress distributions in monolimbs with
different shank designs at different walking phases were reported. Using distortion energy theory,
prediction of possible failure was performed. The effect of the stiffness of the monolimb shanks on
the stress distribution at the limb-socket interface was studied. The results showed a trend that the
peak stress applied to the limb was lowered as the shank stiffness decreased. The information is
useful for future monolimb optimization.
Keywords: finite element analysis, interface stress, monolimb, shank flexibility, structural integrity,
transtibial prosthesis
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INTRODUCTION
Transtibial amputees usually demonstrate some gait abnormalities such as lower walking speed (1),
increased energy cost (2) and asymmetries between legs of unilateral amputees in terms of stance
phase time, step length and vertical peak force (3). It is believed that the gait abnormalities are
mainly due to the loss of active dorsiflexion and plantarflexion motions of the ankle joint (4).
Prostheses have been designed to compensate for the loss of motions at the foot by incorporating
energy storing and releasing (ESAR) capabilities using flexible keels or shanks. The Seattle footTM
and FlexFootTM are examples of ESAR prosthetic components. Previous research suggested that
many amputees subjectively prefer ESAR prosthetic feet to conventional SACH feet on normal and
fast walking (5, 6). However, many amputees still utilize the simple SACH feet because of their
lower cost.
A “Monolimb” prosthesis design using a conventional prosthetic foot such as SACH foot perhaps is
an alternative to ESAR prosthetic feet if properly designed, providing elastic response of the shank
(7), at the same time lower the total prosthetic weight and cost. It is a kind of trans-tibial prosthesis
having the socket and the shank molded into one piece of thermoplastic material. Different names
have been used for this kind of prosthesis such as endoflex (7), total thermoplastic prosthesis (8) and
ultra-light prosthesis (9). Due to the elasticity of thermoplastics, the shank can deform leading to
simulated dorsiflexion and plantarflexion of the prosthetic foot. By proper use of material and
structural design, it is possible that the shank deformability may be altered such that natural ankle
joint motions are mimicked. At the same time, structural integrity should be maintained without
permanent deformation and buckling of the prosthesis. Changes of shank flexibility may alter the
stress distribution at the prosthetic socket-residual limb interface which is related to the comfort
perceived by the amputees (10). Up to now there is no clear guideline on the shank designs of
monolimbs. In order to optimize the design of monolimb and maximize comfort, comprehensive
understanding of the deformation and stress at the shank of the monolimb during walking and the
effect of the shank flexibility on stress distribution at the interface between socket and limb are
essential.
In general there are two approaches to investigate the shank deformation and its effect on socket-limb
interface stress: experimental measurements and theoretical analyses. Experimental measurements
require the use of stress/strain sensors attached to appropriate positions of the shank and the socket
inner surface. Theoretical analyses such as finite element (FE) methods, which have been widely
used in lower limb prosthetics in the past decade, can be useful to study the deformations and
stresses. The advantage of the use of FE analysis is that stress, strain and motion in any parts of the
model can be predicted and parametric analyses can be performed easily without the need to fabricate
prostheses. In previous FE models, focus was put on investigating into the variation of stresses
distributed at the limb-socket interface under different socket modifications (11, 12), material
properties of the sockets (11, 13) and liners (14) and frictional properties at the interface (15). The
deformability of the prosthesis and the effect of shank deformation on interface stresses, however,
received little attention.
The aim of this paper is to describe the development a FE model which was used to study the
interface stress between the limb and socket, shank flexibility and possible failure of the prosthesis.
Different shank geometries were used and their effects on limb-socket interface stresses were studied.
METHODS
A FE model was developed for a right-sided unilateral transtibial amputee subject to determine the
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stresses in the monolimb during walking and the effect of the shank stiffness on interface stresses at
the limb-socket interface. The subject was 55 years old and 81kg in weight who have experience in
using monolimbs. Contact between the limb and the socket was simulated considering pre-stress
when the limb was donned into a shape-modified socket and friction/slip using automated contact
technique. Our previous FE analyses have showed the importance of the consideration of pre-stress
in predicting interface stresses at loading stage (16,17). Proximal region of soft tissue and the bones
were fixed, and loading was applied at the prosthetic foot according to gait analysis data (17-19).
Geometries
The geometries of the bones and their positions relative to the limb surface were obtained from
magnetic resonance images (MRI) on the subject. Outlines of bones were identified in Mimics 7.1.
The residual limb surface was obtained by digitizing a loose plaster cast using the BioSculptorTM
system. Bone geometries were assembled into the residual limb according to the MRI. A prosthetist
using ShapeMakerTM 4.3 prepared the geometry of the monolimb, by applying built-in, shape-
rectification template, as shown in Figure 1, to the digitized limb surface and aligning a shank and
blending smoothly to the socket end. Different geometries of shanks (Figure 2) were designed for
analysis. The whole monolimb was assigned 4 mm thickness. The geometry of the prosthetic foot
was based on direct measurement of a Kingsley SACH foot (length 250mm) and was added to the
distal end of the shank. The foot was partitioned into two regions: the wooden keel, and the
surrounding rubber foam. Although the shank geometry was varied in different designs, the relative
positions of the prosthetic foot to the socket were the same. The model in its entirety, as shown in
Figure 3a, was exported to ABAQUS version 6.3 (Hibbitt, Karlsson & Sorensen, Inc., Pawtucket,
RI). A FE mesh with 3D tetrahedral elements were built using ABAQUS auto-meshing techniques.
The number of elements assigned varied among different monolimb designs ranging from 37,836 to
38,565.
Material properties
In this preliminary study, the mechanical properties of the materials were assumed to be linearly
elastic, isotropic and homogeneous. The estimated Young’s modulus was 200kPa (15) for soft
tissues and 1500MPa (20) for the monolimb structure following the mechanical property of
polypropylene homopolymer. Poisson’s ratio was assumed to be 0.45 for soft tissues and 0.3 for
monolimb. The prosthetic foot was partitioned into a keel region and surrounding rubber foam and
were assigned Young’s moduli 700MPa and 5MPa respectively. Poisson’s ratio was assumed to be
0.3 for the two regions of the prosthetic foot.
Boundary conditions and analysis steps
The four bones were given fixed boundaries. Fixed boundary was also given to proximal region of
the soft tissue as shown in Figure 3. The fixed region of the soft tissue was away from the socket so
that the boundary condition would not have significant effect on interface stresses. The bones and
soft tissues were modeled as one body with different mechanical properties. The residual limb and
socket were modeled as two separate structures and their interaction was simulated using automated
contact methods. The distal surface of the shank and the top surface of the prosthetic foot were tied
together by rigidly connecting the nodes between the two surfaces where they contact. For
simplification, it was assumed there was no foot clamp adaptor holding the shank onto the prosthetic
foot.
There were two phases in the analysis. The first phase was to simulate the interaction produced by
donning the limb into the prosthetic socket. At this phase, the external surface of the monolimb
together with the bones and the soft tissue around the femur were fixed. Initially, some regions of the
limb penetrated into prosthetic socket, as shown in Figure 3b, because of the socket rectification.
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Automated contact method was employed and the solver in ABAQUS automatically moved the
penetrated limb surface onto the inner surface of the socket. Stresses were developed on both the
inner surface of the socket and the residual limb over the overlapped regions (16,17).
At the second phase, the pre-stresses and the deformations calculated in the first phase were kept.
The fixed boundary constraint previously added to the external surface of the monolimb was
removed. External loadings were applied at the prosthetic foot to simulate the participating subject
walking. Stiffness changes upon large deformations, known as geometrical nonlinearity, were
considered. Three load cases were applied separately at the centers of pressure on the plantar surface
of the foot according to gait analysis data of the same amputee (18, 19) to simulate heel strike,
loading response and heel off of gait. The three loading conditions were respectively 8%, 19% and
43% of stride. The center of pressure was obtained by projecting the positions of center of pressure
calculated on the force platform onto the plantar surface of the foot. Kinematic data of the limb and
monolimb and ground reaction forces were obtained from the Vicon Motion Analysis System and a
force platform respectively. The magnitude, position and direction of the applied load were listed in
Table 1. The loadings were assumed to be the same for different shank designs at the same loading
conditions. This assumption was based on previous research showing that the ground reaction forces
varied little with the use of different stiffness of prosthetic feet (21, 22). Coefficient of friction (
μ
) of
0.5 was assigned for socket-limb interface (15, 23). Sliding was allowed only when the shear stress
at the interface exceeded the critical shear stress value τ > τcrit =
μ
p, where p is the value of normal
stress. The analysis was performed with different shank designs of the monolimb as shown in Figure
2.
RESULTS AND DISCUSSIONS
Figure 4 shows the von Mises stress distribution in the monolimb with circular shank (design A
shown in Figure 2) over the three loading conditions. At heel strike and loading response, peak von
Mises stresses fall on the antero-proximal region of the shank. Whilst at heel off, peak von Mises
stresses fall on the antero-distal region of the shank. The stresses are smaller at heel strike because
of the lower ground reaction forces and shorter moment arm from the load line of the ground reaction
force to the shank, and reach the highest, which is 11.2 MPa for design A, at heel off. Using
distortion energy theory, which is widely used in predicting failure of ductile materials (24), failure is
predicted to occur if the von Mises stress is equal to or greater than the uniaxial failure stress. Yield
stress of polypropylene homopolymer, which is 35MPa (20), is considered to be the uniaxial failure
stress based on the fact that the design of monolimb is deemed unacceptable if the permanent
deformation occurs changing the alignment of prosthetic foot relative to the socket. As the peak von
Mises stresses are much lower than the yield stress of the thermoplastic material, failure is predicted
not to occur during level walking for that design. Table 2 shows the values of prosthetic foot
dorsiflexion angles. Foot dorsiflexion angles are defined in this paper as the angle changes between
the transverse plane and the flat surface of the prosthetic foot attached to the shank (Figure 5) after
external loadings were added. The “foot dorsiflexion angles” takes into account the motions of the
prosthetic foot due to deformation of the shank and the movement of the whole monolimb with
respect to the residual limb. For monolimb design A, the prosthetic foot dorxiflexes to 4.2 degrees at
heel off which is much lower than the normal foot dorsiflexion angle at around 10 degrees (25)
during the period of heel off.
From the above results, there is space for the increase in shank flexibility as the peak von Mises
stresses were much lower than the yield stress of the material, the shank appears rigid for the circular
shank having 48mm outer diameter and previous research showed that shank flexibilities can enhance
gait performance (7, 9). Shank flexibilities were altered in this study by changing the cross sectional
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geometry of the shank as shown in Figure 2. Table 2 shows the locations of peak stress at the shank
and compares the magnitudes of peak von Mises stresses and foot dorsiflexion angles among
different shank designs at the three loading conditions. Reducing the antero-posterior dimension of
the shank at the distal end (design B) leads to increases in flexibility of the shank. High von Mises
stresses (Table 2) and major deformation (Figure 5a) occurs at the distal end of the shank of
monolimb design B at loading response and heel off. The peak von Mises stress for design B
increases to 30.8 MPa (Table 2) at heel off which is predicted to be lower than the yield stress of the
material and hence the design meets the strength requirement. Further investigation is required to
look into the fatigue life of the monolimb under this stress level. Foot dorsiflexion angle reaches
11.5 degrees comparable to that of normal foot at heel off. The increase in foot dorsiflexion angle at
heel off could be the main contribution on the improved gait efficiency using prosthesis with flexible
shank as suggested by previous researchers (7, 9, 26). Reducing the antero-posterior dimension of
the shank at proximal end forming a uniform cross sectional elliptical shank (design C) gives further
increase in the flexibility. However, some material yield is predicted to occur at heel off for the
elliptical design as it is estimated that the peak von Mises stress was slightly greater than 35 MPa.
Figure 5b shows the predicted deformation of monolimb design C.
It is noted that the measurement method of ankle motion used in this study was not same as the one
used in gait analysis. Ankle motion was described in this study by the angle changes of the top
surface of the solid wooden keel of the prosthetic foot in the sagittal plane. This measurement
method placed emphasis on the motion of the prosthetic foot due to shank deflection which was the
primary interest of this study. The measured foot motion was apparently unaffected by the
deformation of the rubber foam at the plantar region of the prosthetic foot and the possible motion
between the shoe and the foot. In gait analysis, ankle motions are commonly measured according to
the reflective markers attached to the prosthesis and the shoe. Motion of the foot-shoe complex and
the compression of the rubber foam could both contribute to the foot motion.
Previous gait analysis studies show a brief external plantarflexion moment early in the stance phase
as the line of action of the ground reaction force passes posterior to the ankle joint, followed by
dorsiflexion moment when the ground reaction force shifts anteriorly (25). The results in this study,
however, show that the prosthetic foot dorsiflexed at all the three loading conditions. At heel strike,
the line of action of the ground reaction force as usual passes posterior to the ankle joint which tends
to plantarflex the prosthetic foot. However, as the force line passes anterior to the proximal shank
and the knee joint, the foot dorsiflexion angle, defined as the angle changes between the transverse
plane and the flat surface of the prosthetic foot attaching to the shank, is positive given the
deformability of the shank as well as the motion of the monolimb relative to the residual limb. The
magnitudes of the dorsiflexion angles are small at heel strike for the three monolimb designs.
Another important aspect of this study is to investigate the stress distribution at the limb-socket
interface with varying monolimb flexibility. Figure 6 shows the normal stress distributions of the
limb at heel strike, loading response and heel off using the monolimb design A. High pressure falls
on mid-patellar tendon (MPT), anterolateral tibia (ALT), anteromedial tibia (AMT) and popliteal
depression (PD) regions where socket undercuts were made. The three loading conditions caused
extension of the monolimb relative to the residual limb. The extension moment is consistent with
previous gait study showing that transtibial amputees demonstrated an external knee extension
moment almost throughout the stance phase of the gait as they tended to move the body center of
mass more anteriorly (27). Due to the extension moment of monolimb and the inward budge of the
patellar bar, the stresses are greater in patellar tendon region than popliteal depression region. The
presence of laterally directed ground reaction force (26) explains the higher pressure in anterolateral
tibia than anteromedial tibia regions. High resultant shear stress, which is the combination of
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longitudinal and circumferential components of shear stresses in the plane of contact interface, is
predicted at the four critical regions with socket undercuts. The peak stresses predicted in the FE
model are in the range of the clinical measurements (28, 29).
The patterns of the normal and shear stress distribution are similar among the three different shank
designs at the same loading conditions but differ in peak stress values. Figures 7 and 8 compare the
peak normal and resultant stress distribution over the four critical areas among different shank
designs. There is a tendency that increases in shank flexibility led to general decreases in peak
stresses applied onto the residual limb. The tendency could be explained from a total energy point of
view. Deformation of the prosthesis absorbs some energy, just like ESER prosthetic foot absorbing
some potential energy, causing the reduction of the energy actually transferred to the residual limb.
The magnitude of stresses applied onto the skin surface of the residual limb are related to comfort
perceived by amputees (10). The reduction of stresses could explain improved comfort of using
prosthesis with flexible components (7, 9, 11).
It was assumed in the model that the soft tissue was a passive structure. However, in the real case the
muscles at the residual limb would have some degree of contractions during walking. Muscle
contractions leading to stiffness changes at different regions of the limb could alter the stress
distribution at the limb-socket interface. Little is known about the effect of muscle contractions on
interface stresses because most FE models did not consider muscle contraction (11-15). The
inclusion of muscle contraction in FE model requires the investigation of the timing and intensity of
muscle contraction at the residual limb during walking, the relationship between muscle contraction
and stiffness, and the muscle geometry from imaging data. The difference in prediction of interface
stress between a passive soft tissue structure and a soft tissue with muscle contraction deserves
further investigation.
As far as the fabrication method is concerned, monolimb is traditionally fabricated by drape molding
a heated thermoplastic sheet onto the model composed of a shape-modified residual limb plaster
model and a pylon giving the shape of socket and shank of the monolimb (7,9). A liner can be added
within the socket which could help distribute stresses more evenly at the limb-socket interface and
closing the “hole” at the distal end of the socket. However, a liner could produce some problems
such as hygiene problems (sweat absorbing) and requirement of frequent maintenance. We have
some experience of fitting patients with monolimbs which do not have liners and do not encounter
major fitting problems. For those reasons a liner was not added in this FE model. Under this
fabrication method, the wall-thickness of the thermoplastic material is almost uniform. Adjusting the
cross-sectional geometry of the shank of a monolimb appears to be the most effective method of
altering the flexibility of the monolimb.
It is possible the fabrication processes be performed using computer-aided design/computer-aided
manufacturing (CAM/CAM) system. The residual limb shape can be digitized, and socket shape-
modification and positioning of the shank can be designed in a prosthetic CAD software, such as
ShapeMakerTM (30). The CAD data can then be sent to a rapid prototyping machine for fabrication.
The use of rapid prototyping machine to fabricate prosthetic socket have been reported in the
literature (31, 32). Using CAM/CAM technique, monolimbs can be fabricated with tailored varying
wall thickness and geometry of the shank. However, this fabrication method is much expensive.
In future studies, improved characterization of material properties of soft tissues and interface contact
conditions between the skin and the socket will be pursued. Gait analysis and clinical measurement
of the stresses at the limb-socket interface and prosthesis will be performed to validate the model.
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Fatigue life of monolimbs under repeated loading will be investigated. The FE models will be served
as an important tool in the process of optimizing prostheses with flexible shanks. Further parametric
analysis of the model will be performed for the optimization.
CONCLUSION
Little has been suggested about the design of monolimb due to the lack of understanding of the
deformation and strength of the shank under loading, and the effect the shank deformability on
comfort. In this study, a finite element model was developed which can contribute to 1) the
prediction of shank deformability of monolimbs during walking without actual prosthetic fitting and
direct measurement 2) the prediction of stress distribution at the shank and the inspection of possible
failure of the prosthesis which serves as a reference for future monolimb design and optimization,
and 3) the better understanding of the effect of shank flexibility on socket-limb interaction. The
improved understanding of monolimb structural behavior could promote further optimization of the
design of monolimbs.
ACKNOWLEDGEMENTS
The work described in this paper was supported by The Hong Kong Polytechnic University Research
Studentship and a grant from the Research Grant Council of Hong Kong (Project No. PolyU
5200/02E).
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Table 1. Three loading conditions analyzed in the FE model
Loading
conditions
(% of stride)
Vertical
force (N) Antero-
posterior
force (N) *
Medial-
lateral force
(N) #
Center of
pressure
distance from
back of the
heel (cm)
Heel strike (8%) 480 -67 -10 5.3
Loading
response (19%) 946 -143 69 12
Heel off (43%) 804 57 65 17.3
* positive value indicates anterior-directed force
# positive value indicates lateral-directed force
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Table 2. Comparisons of peak von Mises stresses and foot dorsiflexion angles among three different
shank designs at three loading conditions
Location of the
shank having peak
von Mises stress
Peak von
Mises
stress
(MPa)
Foot
dorsiflexion
angle
(degrees)
Design A Anterior-proximal 3.2 0.5
Design B Anterior-proximal 4.4 2.0
Heel
strike Design C Anterior-proximal 6.9 2.2
Design A Anterior-proximal 8.8 2.7
Design B Anterior-distal 18.0 5.2
Loading
response Design C Anterior-proximal 27.2 12.2
Design A Anterior-distal 11.2 4.2
Design B Anterior-distal 30.8 11.5
Heel off Design C Anterior-distal 36.7 16.3
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CAPTIONS
Figure 1. Socket rectification template. Patella (Pa), patellar tendon (PT), fibular head (FH),
anteromedial tibia (AMT), anterolateral tibia (ALT), tibial crest (TC), fibular end (FE), tibial end
(TE) and popliteal depression (PD) are the regions where rectifications were applied. The numbers
shows the maximum depth/height (in millimeter) of undercuts (negative values) or build-ups
(positive values) over the regions.
Figure 2. Three different shank designs analysed in the FE model. Design A – circular shank with
outer diameter 48mm; Design B – proximal end of the shank being circular with outer diameter
48mm, the cross section becoming elliptical towards the distal end as the anteroposterior dimension
linearly reduced to 28mm; Design C – elliptical shank with outer diameter 28mm.
Figure 3. (a) Geometries of bones, residual limb, monolimb and prosthetic foot; (b) Closer look at the
residual limb-prosthetic socket showing that some regions of the undeformed residual limb
penetrated into the socket due to socket rectification.
Figure 4. Von Mises stress distribution at the monolimb with the 48mm diameter circular shank
(design A) at (a) heel strike, (b) loading response and (c) heel off.
Figure 5. Deformation of shank of (a) design A, and (b) design B at the three loading conditions.
Figure 6. Anterior and posterior views of normal stress distribution at (a, b) heel strike, (c, d) loading
response and (e, f) heel off using monolimb with 48mm diameter circular shank
Figure 7. Comparison of normal stress distribution at mid-patellar tendon (MPT), anterolateral tibia
(ALT), anteromedial tibia (AMT) and popliteal depression (PD) regions at the instance of (a) heel
strike, (b) loading response and (c) heel off using the three different shank designs
Figure 8. Comparison of shear stress distribution at mid patellar tendon (MPT), anterolateral tibia
(ALT), anteromedial tibia (AMT) and popliteal depression (PD) regions at the instance of (a) heel
strike, (b) loading response and (c) heel off using the three different shank designs
13
Figure 1
14
Figure 2
183mm
341mm
48mm
Uniform cross
section over
the shank
Design A
A
nterio
r
Posterior
Design B
Shank proximal
end
48mm
48mm
28mm
Shank distal
end
48mm
28mm
Uniform cross
section over
the shank
Design C
A
nterio
r
Posterior
183mm
341mm
A
nterio
r
Posterior
183mm
341mm
15
Figure 3
Patellar tendon
Popliteal
depression
Bones Prosthetic socket
Residual limb
Residual limb
Bones
Monolimb
Prosthetic foot
(a) (b)
Loading added
at the plantar
surface of the
foot
Proximal region
of the limb given
fixed boundary
16
(a) (b) (c)
Figure 4
3.2MPa 8.8MPa 11.2MPa
17
Figure 5
Heel strike Loading
response Heel off
Heel strike Loading
response Heel off
(a)
(b)
5.2 degrees
11.5 degrees 16.3 degrees
12.2 degrees
Dorsiflexion
2 de
g
rees
Dorsiflexion
2.2 de
g
rees
18
Figure 6
(a) (b)
(c) (d)
(e) (f)
A
nterior view Posterior view
287 kPa
123 kPa
70 kPa
142 kPa
370 kPa
337 kPa
82 kPa
152 kPa
354 kPa
206 kPa
74 kPa
177 kPa
MPa
MPa
MPa
Heel strike
Loading
response
Heel off
19
0
50
100
150
200
250
300
MPT ALT AMT PD
Regions
Pressure (kPa)
Design A
Design B
Design C
(a) Heel strike
0
50
100
150
200
250
300
350
400
450
MPT ALT AMT PD
Regions
Pressure (kPa)
Design A
Design B
Design C
(b) Loading response
0
50
100
150
200
250
300
350
400
450
MPT ALT AMT PD
Regions
Pressure (kPa)
Design A
Design B
Design C
(c) Heel off
Figure 7
20
0
20
40
60
80
100
MPT ALT AMT PD
Regions
Stress (kPa)
Design A
Design B
Design C
(a) Heel strike
0
20
40
60
80
100
120
140
MPT ALT AMT PD
Regions
Stress (kPa)
Design A
Design B
Design C
(b) Loading response
0
20
40
60
80
100
120
140
160
MPT ALT AMT PD
Regions
Stress (kPa)
Design A
Design B
Design C
(c) Heel off
Figure 8
