J. Biomedical Science and Engineering, 2011, 4, 762-768
doi:10.4236/jbise.2011.412094 Published Online December 2011 (http://www.SciRP.org/journal/jbise/ JBiSE ).
Published Online December 2011 in SciRes. http://www.scirp.org/journal/JBiSE
Analysis of trans tibial prosthetic socket materials using finite
element method
Prasanna Kumar Lenka1, Amit Roy Choudhury2
1Department of Rehab Engineering, NIOH, Kolkata, India;
2Department of Applied Mechanics, BESU, Shibpur, India.
Received 24 August 2011; revised 19 October 2011; accepted 14 November 2011.
ABSTRACT
The objective of this work was to analyze in a para-
metric study for optimum design solution of pros-
thetic socket material by finite element method. A
realistic three-dimensional finite element model of
the PTB socket was developed to find out the stress
distribution pattern under physiologically relevant
loading condition during normal walking. The CAD
model of the rectified socket was collected from a
CMET 250 non-tactile high accuracy (0.06 mm)
white light scanner and analyses were carried out
using finite element Method in ANSYS®. All struc-
tural materials used in the analysis were assumed to
be linearly elastic, homogeneous and isotropic. Dif-
ferent materials were used for socket and only poly-
propylene was used for socket adopter. Analysis was
prepared at 2 mm, 3 mm, 4 mm, 5 mm & 6 mm
thickness of socket in different materials commonly
used in developing countries. The bottom line of
socket was made to zero displacement constraints
and vertical loads in relation to stance phase of gait
cycle were applied under static condition at the pa-
tella tendon brim. The 3 mm laminated composite
sockets was found to be optimum in terms of strength,
weight and factor of safety.
Keywords: Finite Element Method; Transtibial Prosthe-
sis; Socket; Polymer
1. INTRODUCTION
The major contribution towards successful fitment of
prosthesis may be obtained by comprehensible under-
standing the biomechanical structure of socket and its
material, weight, thickness in particular to fulfill the de-
sirable load distribution in soft tissues and bone of re-
sidual limb. One most commonly used socket design in
developing countries, that has shown success in balanc-
ing the biomechanical principles and load bearing fac-
tors of the residual limb anatomy for persons with tran-
stibial amputation (TTA) is the patellar tendon bearing
(PTB) socket, developed following the World War II at
the University of California, Berkeley in the late 1950 s
[1,2]. The Finite Element Method (FEM) has been used
widely in biomechanics to predict stress and strain in
complicated systems and have been identified as a useful
tool in understanding load transfer in prosthesis [3]. The
FEA Models have been used to study the effects of the
inertial loads and contact conditions on the interface
between prosthetic socket and residual limb of an ampu-
tee during the gait [4,5]. The FEA has also been used as
a tool for parametric study and evaluation of prosthetic
components [6,7]. Most of the previous studies have
attempted to investigate socket interface pressure meas-
urement, friction-related phenomena, computational
modeling, and real-time patient specific internal stress at
the residuum [8-23]. The biomechanical understanding
of stresses at the residual limb and development of ad-
vanced manufacturing process like CAD/CAM has im-
proved socket design in developed countries. However,
the requirements sockets for TTA in developing coun-
tries are different. Often financial resources are quite
limited and th e functional demand s on prosthetic so ckets
are extreme. It has been reported that the basic factors
which should be considered in developing countries
when selecting socket materials are function, durability,
stability, cost, availability, sustainab ility, climatic condi-
tions, and ease of maintenance [24]. In a survey of ten
years (1994-2004) follow up and repair records of TTA
fitted in one of the national Institutes in India, it was
observed that 66% of total replacement/repair of pros-
thesis occurred due to socket breakage, material failure
and deformation [25]. In a follow up study of HDPE
Jaipur Prosthetic technology, Jensen (2004) et al., re-
ported 50% cases need replacement due to failure of
components [26]. Hence, a further study is required to
analyze structural topology, compliance and biome-
chanics of the socket to predict critical stress zones in

P. K. Lenka et al. / J. Biomedical Science and Engineering 4 (2011) 762-768 763
different socket material in developing countries. This
paper describes the study of structural topology accoun-
ting for the part material and mechanical properties,
weight of the socket, identifying the target deformation
under specific loads, and assessing the feature’s structural
integrity by finite element analysis.
2. MATERIALS & METHOD
A male right sided traumatic trans-tibial amputee, 35
years of age, 156 cm height and 71 kg in weight, par-
ticipated in this study. He had been using an exoskeletal
trans-tibial prosthesis in the last eight years with PTB
socket and SACH foot. The CAD model of glass fiber
composite laminated PTB socket of a traumatic TTA
from developing country was selected for this study. The
analysis was done in ANSYS® software (ANSYS, Inc.
Pennsylvania, USA), version 10.0. The study was ap-
proved by the Institutional Ethical committee in Jan
2009 [25]. The socket thickness was 3 mm and fabri-
cated using glass fiber reinforced composite thermoset-
ting plastic and trimmed based on principle of PTB
socket and the complete assembly is given in Figure
2(a). The CAD model of total surface of socket was
stored using COMET 250 non tactile white light scann er
[27] at Central Mechanical Engineering Research Insti-
tute (CMERI) [28] as shown in Figure 1.
The STL format surface data received from COMET
250 was converted to IEGS format. The detailed and
geometrically accurate three-dimensional finite element
model of socket was developed using the surface data of
original model. Several trials were prepared by increas-
ing number of element during meshing to achieve con-
vergence. The final mesh model using shell 63 and solid
92 is shown in Figure 2( b) .
Among the various types of elements available in the
ANSYS library, the 4-noded (I, J, K, L) elastic shell
(shell63) element was chosen for area mesh generation
of socket. The element has six degrees of freedom at
each node: translations in the nodal x, y, and z directions
(UX, UY, UZ) and rotations about the nodal x, y, and z-
axes (ROTX, ROTY, ROTZ). A reference Shell63 and
solid 92 is shown in Figure 3. The socket area was
meshed with shell63 and adopter volume with solid92.
The solid92 is well suited for irregular shaped solid and
has three degree of freedom (translation in x, y, z direc-
tion). The entire PTB socket model contained 15017
elements (including 1251 contact elements) and 7678
node.
All structural materials used in the analysis were as-
sumed to be linearly elastic, homogeneous and isotropic.
Different materials were used for socket and only poly-
propylene was used for socket adopter. Analysis was done
at different thickness (2 mm, 3 mm, 4 mm, 5 mm and 6
mm) of socket in composite (Glass fiber reinforced
laminated plastic), Polypropylene, High Density Poly-
ethylene (HDPE) and Low Density Polyethylene (LDPE).
Elastic properties (Young’s Modulus (YM), Poisons
Ratio (PR), and Ultimate Strength (US)) of different
materials used in the analysis are shown in Table 1.
A zero displacement constraint was specified at the
bottom of the socket, where rest parts of the prosthesis
were attached. The loading conditions given in Table 2
were quasi-static approximations using experimentally
measured vertical ground reactio n for the prosthetic side
of same subject during walking in self selected speed
using CGD gait Analyzer [29-32]. The total loads were
applied uniformly at all nodes in the patellar br im region
as shown in Figure 2(c), accordingly separate static so-
lutions were prepared for each load using ANSYS pre-
processor.
3. RESULTS
The peak von Mises, shear and principal stress, displace-
ment, rotation in both frontal and saggital plane were
evaluated at importan t pressure tolerance/sensitive areas.
The von Mises stress distributions in 3 mm composite
(a)
(b)
Figure 1. A-COMET 250, B-Side view of during scanning of
stump.
Socket
Pylon
(a) (b) (c
Foot
)
Figure 2. (a) Original prosthesis along with laminated PTB
socket; (b) Meshed model of socket; and (c) Meshed model
long with loading conditions. a
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P. K. Lenka et al. / J. Biomedical Science and Engineering 4 (2011) 762-768 764
Figure 3. Geometry of Shell63 and Solid92.
Table 1. Material properties [5.41].
Material YM (M Pa) PR (g/cm3) Density US (MPa)
Composite 1600 0.39 1.194 144
Polypropylene 1100 0.37 0.91 80
HDPE 800 0.40 0.95 37
LDPE 280 0.41 0.92 25
Table 2. Maximum vertical ground reaction force.
Events of Gait Cycle GRF in Newton(N)
Heel Strike (0% to 15%) 590
Loading Response (15% to 35%) 970
Mid Stance (40% to 6 0 %) 677
Toe off (80% to 100 %) 780
socket over four loading conditions were shown in Fig-
ure 4. The peak von Mises stresses were found at the
anterior proximal region of the socket adopter at heel
strike and loading response. The stresses were less sig-
nificant at heel strike and higher (9.8 MPa) at loading
response.
Following approaches have been discussed to achieve
socket optimization:
1) Analyzing Socket Structural Behavior versus
Thickness: The von Mises stress, von Mises strain &
vector sum of displacement of all materials in different
thickness were analyzed and shown in Figures 6-8.
2) Analyzing Factor of Safety of Socket in Refer-
ence to Thickness: The weight of the socket in different
thickness of composite, polypropylene (PP), HDPE and
LDPE materials were calculated and shown in Table 3.
Figure 4. Von mises stress at heel strike, loading response,
mid stance and toe off (a), (b), (c) & (d) of stance phase in
normal walking at self selected speed.
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P. K. Lenka et al. / J. Biomedical Science and Engineering 4 (2011) 762-768 765
Table 3. Weight of the socket (Grams).
Thickness Composite PP HDPE LDPE
2 mm 140 106 111 107
3 mm 209 160 168 174
4 mm 280 212 214 222
5 mm 350 266 278 269
6 mm 420 320 334 323
3) Analyzing Socket Failure: The Tsai-Hill Criterion
based on the Maximum Distortion Criterion was applied
in this study to predict failure of the socket [33].
2
22 2222
112212
thv TTV v
CS SS    S
Tsai-Hill Criterion,
where Cth is the Tsai-Hill failure coefficient, Sv (Verti-
cal), ST (Transverse), and STL (Shear) are the ultimate
strengths of composite in the vertical, transverse, and
shear directions (frontal plane), respectively as shown in
Table 4. The σ1, σ2, and σ12 are the imposed stresses in
the longitudinal, transver se, and shear di rections. Failu re
is avoided for Cth < 1.
The peak shearing stress at loading response was 3.7
MPa in frontal plane, which occurred at the lateral sur-
face of the socket especially in line of shaft of fibula and
socket adopter. The maximum displacement was oc-
curred at infra-patellar region in anterior-posterior direc-
tion. The maximum rotation in transverse plane was es-
tablished in anterior medial and posterior medial proxi-
mal border of the socket. Total rotation was maximum in
proximal border of the socket and minimum at the distal
border. The results of von Mises strain and vector sum
of displacement during heel strike was recorded and
shown in Figures 7 and 8. The von Mises strain was
found maximum at the bottom line of the socket. Peak
shear strain was indicated at fibular head and patellar
tendon in the AP direction. A total of 80 (4 No. of Load s
X 4 No. of Materials X 5 No. of Thickness) FEA solu-
tions were analyzed for design optimization. The Von
Mises stress patterns were similar for all materials and
the values made a parabolic relationship with thickness
expect for LDPE. The shear stress in frontal plane and
saggital plane decreased in all materials in the increasing
order of thickness. The vector sum of displacement was
higher in LDPE at all thickness and the displacement of
5 mm LDPE was nearly equal to 2 mm composite.
4. DISCUSSION
One of the most interesting results in FE analysis indi-
cated that the pressures tolerant areas of PTB socket
received more weight, and the results were agreeable to
basics biomechanics of PTB socket as discussed by rec-
tification template from university college of London34.
Von Mises stress was recorded minimum (0 to 50KPa)
at the pressure sensitive area such as tibial tuberosity,
Patellar border, fibular head and tibial crest and the val-
ues shown in Figure 5. The computed stress at patellar
tendon (173 KPaa) and popliteal area (79 KPa) were
measured and found to be in the range of previously re-
ported range of 380 - 200 and 175 - 80 KPa respectively
in a published FEM based analysis[8,18,19] and experi-
mental analysis [35-39].
4.1. Case-1 (In Reference To Thickness of the
Socket)
The von Mises stress patterns in all materials expect
LDPE were found inversely proportional to thickness as
shown in Figure 6. However the stress and stress varia-
tion were higher in case of 2 mm & 3 mm thickness and
Table 4. Tensile and compressive strength of glass FRP, Hahl
et al. (2000) [33].
Strength in M PaSV S
T S TL
Tension 584 43 44
Compression 803 187 64
Figure 5. Von mises stress in pressure tolerant areas in stance
phase of gait cycle during walking at a self selected velocity in
plane surface.
Figure 6. Von mises stress in different thickness of composite,
polypropylene, HDPE and LDPE at load = 590 N.
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P. K. Lenka et al. / J. Biomedical Science and Engineering 4 (2011) 762-768 766
comparatively very low in case of 4 mm to 6 mm thick-
ness. Thus 3 to 4 mm thickness could be a viable solu-
tion in terms of thickness for all materials. The variation
of von Mises strain & vector sum of displacement of all
material was closely approximated expect LDPE as
shown in & 8. The value of von Mises strain and vector
sum displacement in 2 mm LDPE was observed to be
2.67 times higher than 2 mm polypropylene. The socket
may loss the biomechanical load bearing ability, if dis-
placement of patellar tendon area of socket goes higher
than 4 mm as the depth of slot of patellar tendon varies
from 2 to 4 mm [37]. The results indicated that the
LDPE thickness less than 4mm is not suitable for fabri-
cation of PTB socket.
4.2. Case-II (In Reference To Weight of the
Socket)
The factors of safety of all materials were calculated by
dividing max von Mises stress (at a load of 590N) to
endurance limit (50% of Ultimate Tensile Strength) [38].
A graph between factor of safety and weight of socket in
all materials were shown in Figure 7. During human
locomotion, the joint reaction force at knee joint in-
creases 3 to 4 times than the total weight body weight in
stair climbing and speed walking and load on knee joint
even increases more in jumping and fast running[39].
The total load of knee joint of an amputee passes on the
prosthetic socket during different activities of daily liv-
ing. So, a minimum of 6 factor of safety is desirable to
withstand the loading of socket. The factor of safety of
HDPE and LDPE is just below the level of 5 and it can
be concluded that HDPE and LDPE are not suitable for
prosthetic socket design.
4.3. Case-III (Failure Analysis)
A plot of Cth coefficient was described in Figure 8 for
both tensile and compressive strength. The value of co-
efficient in 2 mm thick composite in tensile load was
0.238016 < 1 with only 5 times factor of safety but
thickness between 3 mm (0.048) to 4 mm (0.0163)
composite has a factor of safety higher than 20 times. It
can be summarized that the optimum solution of com-
posite material of thickness 3 to 4 mm has passed the
Tsai-Hill failure criterion.
The static approximations of for the loading in the
boundary conditions in the present study in the different
events of stance phase were established similar to the
dynamic effect proposed by Jia [3]. All the structural
stress curves at different anatomical regions as per Fig-
ure 5 were indicated a double-peaked shape that com-
pared well with results as reported by Faustino [5]. The
result of peak stress in patellar tendon, junction between
socket and socket adopter and socket bottom line was
Figure 7. Factor of safety in all four materials with respect to
weight of socket.
Figure 8. Tsai-Hill failure coefficient plot for both tensile and
compressive load in composite material at a load-590 N.
agreed to lee [40]. The FEA result showed a maximum
of +0.076 mm displacement at the patellar brim and mi-
nimum of –0.483 mm (In opposite direction) at the pop-
liteal depression. The compression was higher at pop-
liteal fossa than patellar tendon due to soft nature of tis-
sue at popliteal region. Similarly, in medial lateral direc-
tion the displacement was maximum (+0.337 mm) in the
lateral wall of socket and minimum at medial wall of
socket (–0.447 mm). The reason could be abduction of
socket during heel strike in the stance phase of gait cycle.
The FEA simulation result of displacement and rotation
at different portion of socket validated the biomechani-
cal requirement of structural integrity in the PTB socket.
5. CONCLUSIONS
The Finite element analysis established productive in
analyzing PTB socket and parametric analysis investi-
gating the effects of various parameters i.e. material
properties, thickness related to socket design proved
effective. The results summarized that integrating local
compliant features within socket wall can be an effective
methods to distribute maximum stress areas and also to
relief contact pressure between the stump and socket.
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P. K. Lenka et al. / J. Biomedical Science and Engineering 4 (2011) 762-768 767
The design solution obtained from the results can be
used as a reference to choose material for fabrication of
socket in developing countries like India, depending on
the weight, strength, cost and availability. The socket
made up of composite material may be concluded the
optimum solution for PTB socket design. The study ex-
plored further future scope for parametric analysis, in-
vestigating the effects of socket stiffness, rectification
scheme and materials on the interfacial stress distribu-
tions.
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