  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 in 2019; moreover, such solutions are closely
related to those obtained in the vanishing-viscosity limit by Crismale and
Lazzaroni in 2016, for the analogous model where only the viscosity parameter
was present.
