Superimposed finite elastic-viscoelastic-plastoelastic stress response with damage in filled rubbery polymers. Experiments, modelling and algorithmicimplementation

The paper presents a phenomenological material model for a superimposed ela stic-viscoelastic-plastoelastic stress response with damage at large strain s and considers details of its numerical implementation. The formulation is suitable for the simulation of carbon-black filled rubbers in monotonic an d cyclic deformation processes under isothermal conditions. The underlying key approach is an experimentally motivated a priori decomposition of the l ocal stress response into three constitutive branches which act in parallel . a rubber-elastic ground-stress response, a rate-dependent viscoelastic ov erstress response and a rate-independent plastoelastic overstress response. The damage is assumed to act isotropically on all three branches. These th ree branches are represented in a completely analogous format within separa te eigenvalue spaces, where we apply a recently proposed compact setting of finite inelasticity based on developing reference metric tensors. On the n umerical side, we propose a time integration scheme which exploits intrinsi cally the modular structure of the proposed constitutive model, This is ach ieved on the basis of a convenient operator split of the local evolution sy stem, which we decouple into a stress evolution problem and a parameter evo lution problem. The constitutive functions involved in the proposed model a re specified for a particular filled rubber on the basis of a parameter ide ntification process. The paper concludes with some numerical examples which demonstrate the overall response of the proposed model by means of a repre sentative set of numerical examples. (C) 2000 Published by Elsevier Science Ltd. All rights reserved.