Implementation of the strongly pronounced non-linear viscoelasticity of an incompressible filled rubber

  • T. Scheffer
  • F. Goldschmidt
  • S. Diebels


Filled rubber materials regularly show a pronounced non-linear viscoelasticity with very long relaxation times. In this contribution, a phenomenological description for an incompressible carbon black-filled EPDM (ethylene propylene diene monomer) is given, which also shows the abovementioned characteristic behaviour. In order to represent the non-linear viscoelastic material, the relaxation times of the model are chosen not as constant material parameters but as process-dependent functions.

This contribution presents two different realisations of the model’s implementation. At first, this work provides an implementation of the material model, which is able to describe complex geometries and loading conditions. In this realisation, the three-dimensional model is implemented in the open source finite element library deal.II for finite deformations. Hence, real applications can be represented. In an alternative numerical solution, the model is reduced to the single case of uniaxial tension. The model is simplified to scalar equations, which are quite easy to handle for the implementation. This procedure provides a more simple identification process, but it presents the roblem that the model character is extremely restricted for the individual case of uniaxial tension.

For the numerical realisation, at first, special attention has to be turned on the determination of the inelastic part of the kinematics. A detailed evaluation of the necessary evolution equations is provided in this contribution. Finally, he results of the different implementations are compared with respect to different loading conditions, like relaxation tests or cyclic loading.


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