Balanced Viscosity solutions to a rate-independent coupled elasto-plastic damage system

TL;DR

This paper develops a mathematical framework for analyzing a coupled elasto-plastic damage system using vanishing-viscosity methods, extending previous work by incorporating plastic hardening and exploring various solution regimes.

Contribution

It introduces a new vanishing-viscosity approach that includes plastic hardening, providing a comprehensive analysis of the coupled system and different solution concepts.

Findings

Different regimes lead to distinct Balanced Viscosity solutions.

The method extends previous damage-only analyses to include plastic hardening.

The approach offers a rigorous mathematical foundation for complex coupled systems.

Abstract

A rate-independent model coupling small strain associative elasto-plasticity and damage is studied via a 'vanishing-viscosity' analysis with respect to all the variables describing the system. This extends the analysis performed for the same system in [Crismale-Lazzaroni 2016], where a vanishing-viscosity regularization involving only the damage variable was set forth. In the present work, an additional approximation featuring vanishing plastic hardening is introduced in order to deal with the vanishing viscosity in the plastic variable. Different regimes are considered, leading to different notions of Balanced Viscosity solutions for the perfectly plastic damage system, and for its version with hardening.