Supports - Preventive Biomechanics - page 161

Fig. 4.11 Shaded contour plots of a direct stress of the plate compression test model, b direct
stress of hemispherical punch test model (section cut view) and c shear stress of the quad lap
shear test model (arrows indicate loading direction)

evaluated. The continuum mechanical description is based on the strain energy
function ( 3.209 ) for non-linear isotropic hyperelastic highly compressible mate-
rials, which have been shown to be sufficient for soft material representation. The
K IRCHHOFF stress tensor s 0 of such a model is given by (cf. Sects. 3.2 , 3.2.6.4 as
well as index ''0'' which refers to the state of equilibrium elasticity according to
equation ( 3.274 )

n i n i

s 0 ¼ 2 X

X

3 N

l k
a k

k a k i J a k b k

i ¼ 1 k ¼ 1

Identification of the Long-Term Parameters: The test scenarios previously
described with respect to long-term material parameter optimization were FE-
modeled and iteratively simulated in the optimization process. The corresponding
FE-models of the plate compression test, the hemispherical punch compression test
and the quad lab shear test are depicted in Fig. 4.11 .
In all previously described models, foam material was modelled using fully
integrated 8-node first-order incompatible mode continuum elements with an
average element side length of 8 mm for models Fig. 4.11 a, b and 1.8 mm for
model Fig. 4.11 c. All three degrees of freedom for bottom foam sample nodes of
models (a) and (b) were constrained (no difference in simulation results were
observed modelling foam-support contact interactions instead of node constrain-
ing; the latter approach was thus chosen to obtain robust and fast optimization
loops). Indenters were modelled as analytical rigid bodies and the fixtures in model
(c) were assumed to be discretely rigid.
Generally, simulation of the test scenario provides (indenter) force-displace-
ment output whose deviation to the corresponding experimental data are to be
minimized (if necessary simultaneously) by a set of adequate material parameters.
Therefore, the model function values of the quad lab shear test were weighted
since the overall sum of squared residuals was unequally dominated (cf. multi-
objective optimization and objective weighting Sect. 3.4 ) . This imbalance was due
to higher reaction force ranges occurring during the plate compression and
hemispherical punch testing, exceeding force values of the quad lab shear test by
one order of magnitude. In the parameter optimization process, restrictions as
presented in Sects. 3.4 , 3.4.8 - 3.4.11 have been implemented. In the following,
comparison of test data with simulation output for HR-foam material, Fig. 4.12 ,