Inhomogeneous finitely-strained thermoplasticity with hardening by an Eulerian approach

TL;DR

This paper develops an advanced Eulerian finite-strain thermoplasticity model incorporating inhomogeneity, hardening, and thermodynamic consistency, enabling rigorous mathematical analysis and potential applications in complex material simulations.

Contribution

It introduces an inhomogeneous, rate-based elasto-plasto-dynamic model with thermodynamic consistency and a framework for analyzing weak solutions.

Findings

Model ensures energy balance and entropy inequality.

Incorporates isotropic hardening and temperature dependence.

Provides a basis for rigorous existence proofs of solutions.

Abstract

A standard elasto-plasto-dynamic model at finite strains based on the Lie-Liu-Kr\"oner multiplicative decomposition, formulated in rates, is here enhanced to cope with spatially inhomogeneous materials by using the reference (called also return) mapping. Also an isotropic hardening can be involved. Consistent thermodynamics is formulated, allowing for both the free and the dissipation energies temperature dependent. The model complies with the energy balance and entropy inequality. A multipolar Stokes-like viscosity and plastic rate gradient are used to allow for a rigorous analysis towards existence of weak solutions by a semi-Galerkin approximation.