Calculus of Variations and Geometric Measure Theory

V. Crismale - G. Lazzaroni - R. Rossi

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

created by lazzaroni on 12 Apr 2022
modified on 31 Oct 2022


Accepted Paper

Inserted: 12 apr 2022
Last Updated: 31 oct 2022

Journal: Ann. Mat. Pura Appl.
Year: 2022
Doi: 10.1007/s10231-022-01280-0


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.