Biomedical Engineering Reference
In-Depth Information
Table 4.3 Long-term
material parameters of
VE-foam material
l j [MPa]
a j [-]
m j [-]
5.280146E - 03
2.208547E ? 01
1.587915E - 04
1.042675E - 03
2.669817E ? 01
2.855843E - 03
and VE-foam material, Fig. 4.13 , is shown based on optimized long-term material
parameters provided in tables Table 4.2 and 4.3 .
Identification of long-term parameters a k , l k and b k of equation ( 3.274 ) using
model parameter N = 2 is performed via the optimization routine described in
Sect. 3.4 . In the quality functional ( 3.364 ) , f i M (h i , p) is the model function with the
indenter force-displacement relation generated on the basis of ( 3.274 ), f i E and h i
are the measured force and displacement data of the indenter and the coordinates
of parameter vector p with the material parameters a k , l k and b k . According to
( 3.364 ), using the norm parameter m = 2, the following material parameters are
derived, meeting the requirements deduced in Sects. 3.4 and 3.4.8 such as
restrictions based on classical linear theory, the B AKER -E RICKSEN inequalities and
polyconvexity, Tables 4.2 and 4.3 (correlation between m i and b i see ( 3.275 ) ).
In the parameter sets listed above, stable (nominal) strain ranges according to
the D RUCKER stability criterion for the deformation modes of uniaxial compression
and uniaxial tension as well as simple shear are shown:
HR-Foam %
VE-Foam %
Uniaxial compression
Stable for all strains
Stable for all strains
Uniaxial tension
Simple shear
\170 Experiments II: Viscoelasticity (Creep)
Experimental Set Up: To mechanically characterize the time domain viscoelas-
ticity of the foam materials HR and VE (see ''Employed Elastomeric Materials'' in
Sect. , Table 4.1 ), the following deformation modes at constant climatic
conditions (20C; 50% humidity) were performed under constant indenter weights
and gravity loading:
1. plate compression creep tests with a plate mass of 17.0 kg
2. hemispherical punch creep tests (punch: Ø48 mm, indenter mass: HR-foam:
27.0 kg, VE-foam: 3.3 kg
Test (1) encorporated foam specimen loading with a rigid plane plate with
variable weight. Plate displacement over time was recorded. Test (2) was primarily
used to verify the derived parameters under a multiaxial strain state, cf. Fig. 4.14 .
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