Finite thermoelastoplasticity and creep under small elastic strains

TL;DR

This paper develops a thermodynamically consistent mathematical model for finite thermoelastoplasticity with creep, incorporating large displacements and plastic strains, and provides rigorous analysis including existence and convergence results.

Contribution

It introduces a novel model combining small elastic strains with large displacements and plastic strains, and proves mathematical well-posedness and approximation convergence.

Findings

Existence of weak solutions established

Convergence of Galerkin approximations proven

Model is suitable for rigorous mathematical analysis

Abstract

A mathematical model for an elastoplastic continuum subject to large strains is presented. The inelastic response is modeled within the frame of rate-dependent gradient plasticity for nonsimple materials. Heat diffuses through the continuum by the Fourier law in the actual deformed configuration. Inertia makes the nonlinear problem hyperbolic. The modelling assumption of small elastic Green-Lagrange strains is combined in a thermodynamically consistent way with the possibly large displacements and large plastic strain. The model is amenable to a rigorous mathematical analysis. The existence of suitably defined weak solutions and a convergence result for Galerkin approximations is proved.