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

TL;DR

This paper analyzes the asymptotic behavior of a coupled elasto-plastic damage model as viscosity and hardening parameters tend to zero, establishing connections with previous limit solutions in the literature.

Contribution

It rigorously characterizes the singular limits of a complex coupled system, extending previous results to include multiple vanishing parameters and their order of limits.

Findings

Limit evolution coincides with known solutions from 2019

Results connect vanishing-viscosity limits with damage-hardening models

Provides a unified framework for different parameter vanishing regimes

Abstract

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.