Biomedical Engineering Reference
In-Depth Information
Fig. 3.29 Concept of the
direct problem with material
parameters as input signal
parameters identified in Step 3, Table
3.4
are dependent on the set of experimental
data
D
1
which was used as the basis for the identification process. The quality of
the material parameters reflecting this experimental output is the subject in the
verification step, Step-4. If the model, including the material parameters, is capable
of simulating experimental scenarios different from the test comprising data set
D
1
results with test output data set
D
2
derived from individual experiments, is
required.
If both data sets contain pairs of discrete data points
D
1
¼f
x
i
;
y
i
g;
D
2
¼
f
x
j
;
y
j
g
the necessary condition holds that if x
i
= x
j
then y
i
= y
j
. In this process,
the material parameters are independent of data set
D
2
.
In
Sects. 4.3
and
5.3
constitutive equations are introduced to describe foam and
tissue material behaviour. The particular experimental loading scenarios were
designed to cover the maximum strain ranges occurring during body weight
loading in the supine or seated position, with specific body mass. According to the
phenomena experienced during material testing, appropriate material models were
chosen, which were able to qualitatively describe the experienced physical effects.
Material parameters were identified for all involved materials to quantitatively
describe the experimental findings. Basic formulation of constitutive equations as
introduced in Step 2, Table
3.4
was not a subject in this process.
3.4.5 The Direct Problem
In mechanics, a material model consists of a set of constitutive equations which
provide a functional relation between stress and strain measures, as most generally
described through
U F
; h i¼
S
ð
3
:
382
Þ
where S for instance is the C
AUCHY
stress tensor, F is the deformation gradient
tensor, and the parameter vector p represents the material constants contained in
the material equations.
These constitutive equations involve, aside from material equations, displace-
ment-strain as well as balance laws, basically coupled in terms of sets of differ-
ential
equations.
Together
with
geometrical
information,
loading
conditions,
displacement
constraints
and
the
material
parameters,
the
conditions
at
the
