Quasistatic nonassociative plasticity at finite strains

TL;DR

This paper develops a mathematical framework for modeling finite-strain elastoplasticity with nonassociative behavior, introducing measure-valued solutions and proving their existence through regularization and discretization techniques.

Contribution

It presents a novel existence theory for quasistatic nonassociative plasticity at finite strains using measure-valued energetic solutions and regularization methods.

Findings

Existence of measure-valued energetic solutions established.

Regularization via space-time mollification is effective.

Discussion on potential for solutions in function spaces.

Abstract

We investigate finite-strain elastoplastic evolution in the nonassociative setting. The constitutive material model is formulated in variational terms and coupled with the quasistatic equilibrium system. We introduce measure-valued energetic solutions and prove their existence via a time discretization approach. The existence theory hinges on a suitable regularization of the dissipation term via a space-time mollification. Eventually, we discuss the possibility of solving the problem in the setting of functions, instead of measures.