Section 6: Material modelling in solid mechanics - GAMM 2012

Section 6: Material modelling in solid mechanics 9
in a relatively simple form and are able to describe the asymptotic behavior of the inverse Langevin
function in the vicinity of the maximum chain extensibility. Far away from the asymptotic
area the approximation error can be, however, relatively large. In the present contribution we
compare various Padé approximants with the Taylor power series representation of the inverse
Langevin function. To this end, a simple recursive procedure calculating power series coefficients
of the inverse function is proposed. The procedure can be applied to any function which can be
expanded into Taylor series. Within the convergence radius the resulting series of the inversed
Langevin function demonstrates better agreement with the analytical solution than the Padé approximations.
Phenomenological modeling of a polymeric composite
Sebastian Borsch, Albrecht Bertram (Universität Magdeburg)
A composite material consisting of a polymeric matrix material and metallic filler particles is
modeled in a phenomenological way. The isotropic viscoplastic constitutive model is formulated
within the theory of finite deformations. The flow rule is a superposition of two terms. This
approach enables us to simulate the strong backflow behavior during unloading, which can be
observed in various polymeric materials. A quasi-static finite-element simulation has been performed
to compare the model with cyclic tension tests as well as a relaxation test.
Modelling of nanoindentation of polymers with effects of surface roughness and parameters
identification
Zhaoyu Chen, Stefan Diebels (Universität des Saarlandes)
Since the nanoindentation testing technique can measure the properties of extremely small volumes
with sub-m and sub-N resolution from the continuously sensed force-displacement curves,
it also became one of the primary testing techniques for polymeric materials and biological tissues.
The analysis of individual indentation tests using the conventionally applied Oliver & Pharr
method has limitations to capture the hyperelastic and rate-dependent properties of polymers.
Therefore, an inverse method with respect to the experimental testing, based on finite element
simulation and numerical optimisation has been used and evolved. However, nanoindentation is
composed of various error contributions, e. g. friction, adhesion, surface roughness and indentation
process associated factors. These contributions forming the systematic errors between the
numerical model and the experiments will often lead to large errors in the parameters identification.
Therefore, basic investigations and quantification of these influences are indispensable to
characterise the materials accurately from nanoindentation based on the inverse method.
In the present contribution, the characterisation of polymers through nanoindentation with effects
of the surface roughness based on inverse method will be investigated numerically. The boundary
value problems of nanoindentation of polymers are modelled with the FE code ABAQUS R○ .
In contrast to the traditional inverse method, virtual experimental data calculated by numerical
simulations with chosen parameters replace the real experimental measurements. Such a procedure
is called parameter re-identification. In this sense, the finite element code ABAQUS R○ is used as
our virtual laboratory. The model parameters are identified using an evolution strategy based on
the concept of numerical optimisation. The surface roughness effects are investigated numerically
based on the approach utilizing the phenomenological concepts. The surface roughness is chosen
to have a simple representation considering only one-level of roughness profile described by a
sine function. The influence of the surface roughness is quantified associated to the sine curve
parameters as well as to the indentation parameters. Moreover, the real surface topography is