A new thermodynamically consistent continuum model for hardening plasticity coupled with damage

A phenomenological model for hardening–softening elasto-plasticity coupled with damage is presented. Specific kinematic internal variables are used to describe the mechanical state of the system. These, in the hypothesis of infinitesimal changes of configuration, are partitioned in the sum of a reversible and an irreversible part. The constitutive equations, developed in the framework of the Generalised Standard Material Model, are derived for reversible processes from an internal energy functional, postulated as the sum of the deformation energy and of the hardening energy both coupled with damage, while for irreversible phenomena from a dissipation functional. Performing duality transformations, the conjugated potentials of the complementary elastic energy and of the complementary dissipation are obtained. From the latter a generalised elastic domain in the extended space of stresses and thermodynamic forces is derived. The model, which is completely formulated in the space of actual stresses, is compared with other formulations based on the concept of effective stresses in the case of isotropic damage. It is observed that such models are consistent only for particular choices of the damage coupling. Finally, the predictions of the proposed model for some simple processes are analysed.