01385nas a2200145   4500008004100000022001400041245009300055210006900148260000800217300001400225490000800239520092700247100001901174856004601193       2017                        eng d  a1618-189100aGlobally stable quasistatic evolution for strain gradient plasticity coupled with damage0 aGlobally stable quasistatic evolution for strain gradient plasti  cApr  a641–6850 v1963 a<p>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 (J Mech Phys Solids 53:1624–1649, 2005). 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 so-called 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 Crismale (ESAIM Control Optim Calc Var 22:883-912, 2016).</p>1 aCrismale, Vito  uhttps://doi.org/10.1007/s10231-016-0590-7