Numerical approximation of a thermodynamically complete rate-type model for the elastic--perfectly plastic response

TL;DR

This paper introduces a novel numerical scheme for a thermodynamically complete rate-type model of elastic--perfectly plastic response, avoiding traditional decompositions and variational inequalities, and includes temperature evolution.

Contribution

It proposes a new rate-type model without elastic-plastic decomposition and variational inequalities, with a finite element discretization and stability analysis.

Findings

Proved existence of discrete solutions under mesh restrictions.

Established stability properties of the numerical scheme.

Provided computational examples demonstrating the method.

Abstract

We analyse a numerical scheme for a system arising from a novel description of the standard elastic--perfectly plastic response. The elastic--perfectly plastic response is described via rate-type equations that do not make use of the standard elastic-plastic decomposition, and the model does not require the use of variational inequalities. Furthermore, the model naturally includes the evolution equation for temperature. We present a low order discretisation based on the finite element method. Under certain restrictions on the mesh we subsequently prove the existence of discrete solutions, and we discuss the stability properties of the numerical scheme. The analysis is supplemented with computational examples.