Biomedical Engineering Reference
In-Depth Information
Fig. 4.10 Lateral straining of the test sample during plate compression testing: a sample in the
undeformed state and b sample in the deformed state with lateral straining at the edges
Boundary Conditions: During the plate compression test, the surfaces of the
support and plane indenter plate were covered with emery paper. This prevented
(undefined) sliding of the contact surfaces and produced reproducible mechanical
conditions for FE-modelling. This lateral fixation, however, led to a multi-axial
strain field in the foam material adjacent to the contact surfaces and caused
inhomogeneous lateral straining, due to shear stress.
Due to fixation via emery paper in the plate compression test the deformation
mode was not fully homogenous (see Fig.
4.10
). Due to relatively low sample
thickness, compared to the sample cross section, the plate compression test led to
lateral straining of the samples with a Poisson's ratio m = 0, such that a region of
proportional elongation with a plane stress and strain state did not exist. The stress
and strain state is thus three-dimensional. Accordingly, the stress coordinates of
the employed material models are not decoupled in the loading and in the trans-
versal direction. Hence parameter optimization cannot be done analytically (even
in the plate compression case), but must be conducted via inverse FEM (iFEM)
using an appropriate FE-model with precise modelling of the test scenario, and
using the finite element solver to provide the model function values, (see
Sect.
4.2.1.3
). Only at a Poisson ratio of m & 0 is it possible to optimize the material
parameters with decoupled stress coordinates, without employing FEM to solve
the boundary value problem cf. (Schrodt et al. 2005).
In the quad lap shear test, foam specimens were glued to the fixtures using a
thin film of liquid adhesive. This approach is ideal for soft elastomeric foam
materials, due to relatively low forces transmitted through the adhesive layer. The
quad lap assembly permits horizontal movement of the end plates, thus avoiding
extensive normal stress development (P
OYNTING
-effect).
4.2.1.3 Material Identification I: Elasticity
Constitutive Equation: Polymeric soft foams exhibit more or less viscoelastic
behaviour, characterized in particular by hysteresis with force relaxation in the
force-time and force-displacement diagram (cf. Figs.
4.9
,
4.12
and
4.13
). Initially,
the mechanical long-term properties of the equilibrium elasticity of foam materials
HR and VE (cf. outlines given previously in ''Employed Elastomeric Materials'',
Table
4.1
) based on the force-displacement data of Figs.
4.12
and
4.13
are
