Singular limits of a coupled elasto-plastic damage system as viscosity and hardening vanish

The paper studies the asymptotic analysis of a model coupling elastoplasticity and damage depending on three parameters-governing viscosity, plastic hardening, and convergence rate of plastic strain and displacement to equilibrium-as they vanish in different orders. The notion of limit evolution obtained is proven to coincide in any case with a notion introduced by Crismale and Rossi (SIAM J Math Anal 53(3):3420-3492, 2021), moreover, such solutions are closely related to those obtained in the vanishing-viscosity limit by Crismale and Lazzaroni (Calc Var Part Differ Equ 55(1):17, 2016), for the analogous model where only the viscosity parameter was present.