Viscoelastodynamics of swelling porous solids at large strains by an Eulerian approach

TL;DR

This paper develops a comprehensive Eulerian model for large-strain swelling porous solids incorporating viscoelasticity, inertial effects, and buoyancy, with proofs of solution existence and regularity.

Contribution

It introduces a fully Eulerian formulation for viscoelastic swelling porous solids at large strains, including higher-order viscosity and buoyancy effects, with mathematical proof of solution properties.

Findings

Model captures swelling, squeezing, and buoyancy effects.

Existence and regularity of weak solutions are established.

The formulation is suitable for analyzing complex porous solid behaviors.

Abstract

A model of saturated hyperelastic porous solids at large strains is formulated and analysed. The material response is assumed to be of a viscoelastic Kelvin-Voigt type and inertial effects are considered, too. The flow of the diffusant is driven by the gradient of the chemical potential and is coupled to the mechanics via the occurrence of swelling and squeezing. Buoyancy effects due to the evolving mass density in a gravity field are covered. Higher-order viscosity is also included, allowing for physically relevant stored energies and local invertibility of the deformation. The whole system is formulated in a fully Eulerian form in terms of rates. The energetics of the model is discussed and the existence and regularity of weak solutions is proved by a combined regularization-Galerkin approximation argument.