A gradient-extended thermomechanical model for rate-dependent damage and failure within rubberlike polymeric materials at finite strains

Abstract

Rate-dependencies play a crucial role in the mechanical response of polymeric materials. Besides viscoelasticity, many polymers also show pronounced rate-dependent behaviour with respect to damage accumulating within the material. Furthermore, thermal effects and large deformations have to be taken into account when modelling the mechanical behaviour of polymers. Within this work, we propose a novel fully thermomechanically coupled material model for the description of rate-dependent damage combined with viscoelasticity at finite strains. The model is based on the multiplicative decomposition of the deformation gradient into thermal and mechanical parts as well as a further decomposition of the mechanical part into equilibrium and non-equilibrium contributions. To describe the temporal dependencies of the damage evolution, we make use of a Perzyna-type approach. We furthermore show the thermodynamically consistent derivation of stresses and heat sources which arise due to energy dissipations triggered by the inelastic effects within the material. With the given material formulation, we are able to describe both, damage due to creep and due to relaxation in a precise manner. Besides the theoretical aspects, we describe the numerical implementation into finite element software and present numerical studies demonstrating the capabilities of the given model.