Biomedical Engineering Reference
In-Depth Information
To establish the pre-stress condition from donning the limb into the rectified socket, an axial
force of 50 N was applied at the center of the knee. Initially, some nodes on the slave surface (limb
surface) penetrated into the master surface (inner surface of the liner) because of the socket recti-
fications. Under the master-slave contact algorithm, the solver in ABAQUS moved the penetrating
slave nodes onto their corresponding tangent planes of the master surface. Stresses (pre-stresses)
were developed at both the master and slave surfaces over the overlapping regions.
13.2.4 a
nalySiS
of
tHe
e
ffectS
of
p
re
-S
treSS
on
f
full
W
eiGHt
B
earinG
The calculated pre-stresses and the deformations at the pre-stress stage were retained, and a full
body weight (W) of 800 N was added at the tibial plateau (Figure 13.1). There were no artificial
constraints imposed between the master and slave surfaces when they were separated as no inter-
face elements were defined at the interface. When the nodes on the slave surface contacted their
corresponding tangent planes of the liner, the solver constrained those nodes not to penetrate
into the tangent planes and stress was developed at both master and slave surfaces. A coefficient
of friction (
μ
) of 0.5 was assigned for the liner-limb interface (Zhang and Mak, 1999). During
the contact phase, sliding was allowed only when the shear stress exceeded the critical shear
stress value τ > τ
crit
=
μp
, where
p
is the value of normal stress. During the sliding phase, if the
shear stress was reduced and dropped lower than the critical shear stress value, sliding stopped.
It was assumed that the static and kinetic coefficients of friction were the same in this model.
To understand how the pre-stresses influenced the predictions, a second model was built for
comparison, which was the same as the first model except that the initial geometry of the residual
limb copied the shape of the liner and no pre-stress was applied onto the residual limb at the first
analysis step. The change in shape of the residual limb after socket donning was simulated in the
second model; however, no pre-stress existed as there was no overlapping region between the limb
and the liner at initial configuration.
13.2.5 p
rediction
of
i
interface
S
treSS
tHrouGHout
a
G
ait
c
ycle
Loading was simulated over an entire gait cycle. The loads were calculated according to the kine-
matic data of the lower limb and the prosthesis, and the ground reaction forces applied to the pros-
thetic foot measured by a Vicon Motion Analysis System (Oxford Metrics, UK) and a force platform
(AMTI, USA) (Jia, Zhang, and Lee, 2004). The equivalent forces and moments applied at the knee
joint during walking were calculated using inverse dynamics. To simplify the problem during the
calculation of the joint loads, assumptions were made that there was no relative movement between
the residual limb and socket during walking and only inertial effects in the sagittal plane were
considered.
13.3
model FIndIngS
13.3.1 p
re
-S
treSS
e
ffectS
on
f
full
W
eiGHt
B
earinG
When the limb was donned into the socket, high normal stress was produced at the regions where
socket undercuts were made, including the areas around the patellar tendon, popliteal depression,
anteromedial tibial, and anterolateral tibial. Figure 13.4a displays the normal stress distribution
when a full body-weight loading (800 N) was applied with prior pre-stressing. The normal stresses
over regions where socket undercuts were made increased further, up to a maximum of 228 kPa over
the mid-patellar tendon region.
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