A finite elastic–viscoelastic–elastoplastic material law with damage: theoretical and numerical aspects Original Research Article

The present work is concerned with the theoretical formulation and numerical implementation of a new isotropic finite elastic–viscoelastic–elastoplastic material law with Mullins’ damage for rubber-like materials based on a set of dissipation inequalities published recently by the first author. A phenomenological model consisting of an elastic, an elastoplastic branch and N viscoelastic branches connected in parallel is exploited. The total free energy and the total stress are additively decomposed into three parts corresponding to the three types of branches. The damage effect is assumed to act on the three types of branches homogeneously and isotropically. According to the dissipation inequalities the evolution equations of the viscoelastic and elastoplastic branches are directly formulated in terms of the corotational rates of the internal elastic logarithmic strains. It is proved that in the present constitutive setting the internal elastic logarithmic strains are coaxial to the total and trial elastic logarithmic strains. The present theoretical and algorithmic formulations provide an alternative geometric representation of the same constitutive model outlined in [J. Mech. Phys. Solids 48 (2000) 323]. The numerical simulations show that the present material law gives predictions agreeing quite well with the experimental observations and numerical simulations issued in (loc. cit.).