On continuum damage-elastoplasticity at finite strains

A strain-based continuum damage-elastoplasticity formulation at finite strains is proposed based on an additive split of thestress tensor. Within the proposed framework, a hyperelastic extension of the classicalJ ₂-flow theory is developed as a model problem, with a rate-free formulation of the (linear) kinematic hardening law that is free from spurious stress oscillation in the simple shear test. The algorithmic implementation of the coupled damage-elastoplasticity model is shown to reduce to a trivial modification of the classical radial return which is amenable toexact linearization. This results in a closed form expression for theconsistent elastoplastic-damage modulus. The algorithmic treatment of the damage model with no restrictions on the functional forms governing the plastic response is considered subsequently. It is emphasized that objective rates and incrementally objective algorithms play no role in the present approach. A number of numerical experiments are presented that illustrate the performance of the proposed formulation.