Thermomechanics of damageable materials under diffusion:modeling and analysis

TL;DR

This paper develops a comprehensive thermodynamic model for materials experiencing diffusion, phase changes, damage, and heat transfer, with proven existence of solutions for the complex PDE system.

Contribution

It introduces a novel, thermodynamically consistent model that integrates diffusion, damage, phase transformations, and heat effects in solids, with a rigorous existence proof.

Findings

Model applies to diverse systems like metal-hydrogen and ferro-magnetic materials.

Existence of solutions established for the complex PDE system.

Framework accommodates damage, phase change, and thermal effects simultaneously.

Abstract

We propose a thermodynamically consistent general-purpose model describing diffusion of a solute or a fluid in a solid undergoing possible phase transformations and damage, beside possible visco-inelastic processes. Also heat generation/consumption/transfer is considered. Damage is modelled as rate-independent. The applications include metal-hydrogen systems with metal/hydride phase transformation, poroelastic rocks, structural and ferro/para-magnetic phase transformation, water and heat transport in concrete, and, if diffusion is neglected, plasticity with damage and viscoelasticity, etc. For the ensuing system of partial differential equations and inclusions, we prove existence of solutions by a carefully devised semi-implicit approximation scheme of the fractional-step type.