On renormalised solution for thermomechanical problem in perfect - plasticity

TL;DR

This paper establishes the existence of renormalised solutions for a thermo-plasticity model with nonlinear thermal stress and damping, using advanced mathematical techniques to handle integrable dissipation terms.

Contribution

It introduces a novel approach combining truncation, Boccardo-Gallou"et, and monotone methods to prove existence of solutions in complex thermo-mechanical models.

Findings

Proved existence of renormalised solutions for the model.

Handled nonlinear thermal stress without linearisation.

Addressed integrable dissipation in heat equation.

Abstract

We consider the quasi-static evolution of the thermo-plasticity model in which the evolution equation law for the inelastic strain is given by the Prandtl-Reuss flow rule. The thermal part of the Cauchy stress tensor is not linearised in the neighbourhood of a references temperature. This nonlinear thermal part imposed to add a damping term to the balance of the momentum, which can be interpreted as external forces acting on the material. In general the dissipation term occurring in the heat equation is integrable function only and the standard methods can not be applied. Combining truncation techniques and Boccardo-Gallou\"et approach with monotone methods we prove an existence of renormalised solutions.