A novel approach to the heat build-up problem of rubber

It is well-known that rubber exhibits hysteretic behavior and has a low thermal conductivity. The main consequences are the heat generation and heat build-up phenomena which occur in a rubber component when subjected to repeated deformations. The purpose of our work is to estimate the steady-state temperature reached in rubber component when subjected to cyclic deformation. A decoupled strategy for solution of the cyclic thermomechanical problem is adopted. First a hyperelastic mechanical analysis is performed based on the stabilized behavior of the rubber. Then an estimate of the energy converted into heat is made. It is based on an energetic measure of a mechanical cycle and links the hysteretic energy loss to the elastic mechanical variables. It also accounts for mean strains. An experimental investigation has been carried out in order to identify the strength of the heat sources at various temperatures and mean strains. The influence of the Mullins effect on the dissipation is discussed. Finally, the thermal problem is solved and the influence of changes in geometry on the heat equation for finite strains is taken into account with an approximation based on average values over a cycle. The heat build-up law has been validated: heat build-up experiments have been carried out and comparisons with FE calculations have shown the ability of the law to estimate the transient and steady temperature of geometrically complex component subjected to cyclic deformation.