Materialtheorie am Beispiel eines Elastomerwerkstoffes

The object of the theory of materials is the mathematical modelling of the material behaviour on the basis of general principles and systematic methods. To this end, experiments have to be performed on appropriate specimen. Before constructing a constitutive model, the experimental data can be classified from general points of view. Four possibilities are distinguished: the observed material behaviour may be • rate-independent without hysteresis • rate-independent with hysteresis • rate-dependent without equilibrium hysteresis • rate-dependent with equilibrium hysteresis. In the context of material modelling these categories correspond to 4 different theories of material behaviour, namely • Elasticity • Plasticity • Viscoelasticity • Viscoplasticity. In this contribution the properties of cylindrical specimen made of black-filled rubber are investigated. Experiments of tension, torsion and combinations of tension and torsion are carried out. The data suggest rate-dependence and a very small equilibrium hysteresis which can be neglected. Thus, a material model of nonlinear viscoelasticity is designed on the basis of a rheological model, consisting of nonlinear spring and damping elements. In particular, process-dependent viscosities are introduced. This leads to the possibility to represent nonlinear rate-dependence and the influence of the deformation process on the relaxation during a subsequent hold time. Numerical simulations on the basis of identified material parameters illustrate the physical significance of the constitutive equations.

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