Biomedical Engineering Reference
In-Depth Information
Figure 6.8 The maximum pressures obtained from nonlinear analysis against those of linear
analysis. Simulation conditions are similar to that of Figure 6.7
To exemplify the difference between the results obtained from the nonlinear hyperelastic
analysis and those of linearized relationships, we have compared the maximum pressure
values computed for various applied displacements with those that are obtained from
linear analysis.
This comparison, which is depicted in Figure 6.8, reveals that linear analysis shows
higher values and, secondly, that this difference increases with higher deformation loads.
This result is in agreement with the nonlinear behavior of the tested elastomeric material
illustrated in Figure 6.1. This figure demonstrates that, for infinitesimal deformations, a
straight line could be fitted to the experimental data, although, for larger deformations,
this linear fitting can lead to significant errors.
6.4.4 The Effect of Lump Stiffness
The stiffness of the lump and tissue are also effective parameters in the studied case.
Several researchers [3, 5] have used the ratio of Young's modulus of the lump to that
of the soft tissue, ( E L / E T ), to analyze the relative variations of stiffness of lump with
respect to that of the tissue.
This present analysis, considering nonlinear properties for the tissue, on the one hand,
and assuming linear elastic isotropic property for the lump, on the other, makes the com-
parison between the stiffness of the lump and tissue complicated. Therefore, for this part
of the analysis, the linear elastic modulus of the tissue was considered to be E T =15kPa,
close to the values reported for typical soft tissues [20]. Then, the Young's modulus of
the lump, ( E L ) was changed from 15 kPa to 15 MPa. The results, shown in Figure 6.9,
indicate that for a Young's modulus larger than 1.5 MPa there was no discernible differ-
ence in stress profile. Indeed, the difference between the maximum pressures for E L =
150 kPa and E L = 15 MPa is less than 7%. It can be concluded that the system output
is not very sensitive to E L for E L > 10 E T . This is useful in reducing the number of
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