Biomedical Engineering Reference
In-Depth Information
Fig. 5.23 FE-models for separate material parameter optimization (displacement-driven inter-
face nodes): a fat model, b muscle-bone model
O
GDEN
-model valid for non-linear isotropic hyperelastic slightly compressible
materials proved to be valuable. Based on the O
GDEN
-model, the K
IRCHHOFF
stress
Mechanics'',
Sect. 3.2.6.4
,
as well as index '0' which refers to steady state elas-
ticity according to (3.272)]
"
!
#
s
0
¼
2
X
X
X
3
N
3
l
k
k
a
k
i
1
3
þ
k
a
k
J
a
3
k
a
k
j
Þ
2k
1
D
k
JJ
1
ð
n
i
n
i
:
i
¼
1
k
¼
1
j
¼
1
The assumption of slight compressibility refers to outlines given in (Veronda
and Westmann 1970) and (Fung 1993). Constitutive equations of other forms than
the O
GDEN
-law may be used as long as they can describe high deformation and
distortion occurring during tissue indentation. The H
OLZAPFEL
-G
ASSER
-O
GDEN
-
model has been shown to be more adequate for the elastic and viscoelastic tissue
material description, cf.
Sect. 5.2.5.2
.
Long-term Parameter Identification: The basic idea in identifying appro-
priate (long-term) material parameters for skin/fat and muscle, which account for
the test conditions, is to simulate the separate fat and muscle model independently
(cf. Fig.
5.22
a and b), and to parameterize the material coefficients a
k
, l
k
and D
k
in
(3.272). The Poisson's ratio, which is assumed to be m = 0.495 for both fat and
muscle accounting for slight compressibility, was held constant during parameter
optimization. Consequently, D
1
was determined from l
0
and m using (3.273)
4
.
The optimization algorithm coded in Fortran and based on the deterministic
S
IMPLEX
strategy (Spendley et al. 1962) was coupled with the A
BAQUS
FE-solver
(A
BAQUS
Inc., Rhode Island/USA) following the inverse FE-method and is
functional (3.364) represents in the case of (3.272) the indenter force-displacement
relation, the values f
i
E
and h
i
are the measured force-displacement data of the
indenter as well as the material parameter a
k
, l
k
and D
k
which represent the
coordinates of the parameter vector p. The optimization algorithm was subject to
the following constraints setting the norm-parameter m = 2: at each indenter
