Globally Stable Quasistatic Evolution for Strain Gradient Plasticity Coupled with Damage

We consider evolutions for a material model which couples scalar damage with strain gradient plasticity, in small strain assumptions. For strain gradient plasticity, we follow the Gurtin-Anand formulation [19]. The aim of the present model is to account for different phenomena: on the one hand the elastic stiffness reduces and the plastic yield surface shrinks due to material’s degradation, on the other hand the dislocation density affects the damage growth. The main result of this paper is the existence of a globally stable quasistatic evolution (in the socalled energetic formulation). Furthermore we study the limit model as the strain gradient terms tend to zero. Under stronger regularity assumptions, we show that the evolutions converge to the ones for the coupled elastoplastic–damage model studied in [8].