Biomedical Engineering Reference
In-Depth Information
Figure 6.1 Comparison between experimental results and three-term Mooney - Rivlin strain energy
function. The horizontal and vertical axes are engineering strain and engineering stress, respectively
Table 6.1
The constants of two- and three-term Mooney - Rivlin Models (kPa)
Model
N
C 10
C 01
C 11
Residual
Mooney - Rivlin
2
31.33
8.92
-
7.34
Mooney - Rivlin
3
68.49
39.88
5.71
4.7
It should be noted that initially a two-term model was tried. Nevertheless, the three-term
model was preferred due to its better approximation. The numerical values of the constants
for the two- and three-term Mooney - Rivlin models are summarized in Table 6.1.
6.3 Finite Element Modeling
A nonlinear three-dimensional finite element model using ANSYS commercial software
was developed. The 'mixed u-p formulation' was used to solve the problem because of
its superior results in solving hyperelastic incompressible problems compared with the
'pure displacement formulation' [12]. Although the displacement formulation is compu-
tationally efficient, its accuracy is dependent on Poisson's ratio or bulk modulus. In this
formulation, volumetric strain is determined from derivatives of displacements, which are
not as accurately predicted as the displacements themselves. For nearly incompressible
materials, in which Poisson's ratio is close to 0.5 or the bulk modulus approaches infin-
ity, any small error in the predicted volumetric strain will appear as a large error in the
hydrostatic pressure and subsequently in the stresses. This error, in turn, will also affect
the displacement prediction since external loads are balanced by the stresses. This may
result in smaller displacements than expected for a given mesh (which is called locking)
or, in some cases, result in no convergence at all. This problem is also encountered in
 
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