Solvability of an unsaturated porous media flow problem with thermomechanical interaction

TL;DR

This paper proves the existence of solutions for a complex PDE system modeling unsaturated porous media flow with thermomechanical effects, incorporating hysteresis effects in plasticity and capillarity.

Contribution

It introduces a mathematical framework for solving a coupled PDE system with hysteresis operators in the context of thermomechanical porous media flow.

Findings

Existence of solutions under specific assumptions

Inclusion of hysteresis operators in the model

Framework applicable to thermomechanical porous media

Abstract

A PDE system consisting of the momentum balance, mass balance, and energy balance equations for displacement, capillary pressure, and temperature as a model for unsaturated fluid flow in a porous viscoelastoplastic solid is shown to admit a solution under appropriate assumptions on the constitutive behavior. The problem involves two hysteresis operators accounting for plastic and capillary hysteresis.