Dissipative heating of elastomers: a new modelling approach based on finite and coupled thermomechanics

Abstract

Especially in the automotive industries, elastomers take an important role. They are used in different types of bearings, where they inhibit vibration propagation and thereby significantly enhance driving performance and comfort. That is why several models have already been developed to simulate the material’s mechanical response to stresses and strains. In many cases, these models are developed under isothermal conditions. Others include the temperature-dependent mechanical behaviour to represent lower stiffness’s for higher temperatures. In this contribution it is shown by some exemplary experiments that viscoelastic material heats up under dynamic deformations. Hence, the material’s properties change due to the influence of the temperature without changing the surrounding conditions. With some of these experiments, it is shown that a fully coupled material model is necessary to predict the behaviour of bearings under dynamic loads. The focus of this contribution lies on the modelling of the thermoviscoelastic behaviour of elastomers. In a first step, a twofold multiplicative split of the deformation gradient is performed to be able to describe both mechanical and thermal deformations. This concept introduces different configurations. The stress tensors existing on these configurations are used to formulate the stress power in the first law of thermodynamics which allows to simulate the material’s self-heating. To formulate the temperature dependency of the mechanical behaviour, the non-equilibrium part of the Helmholtz free energy function is formulated as a function of the temperature and the deformation history. With the introduced model, some FE calculations are carried out to show the model’s capability to represent the thermoviscoelastic behaviour including the coupling in both directions.