Finite-strain poro-visco-elasticity with degenerate mobility

TL;DR

This paper develops a mathematical model for finite-strain poro-visco-elastic solids incorporating nonlinear mobility, proving the existence of solutions and addressing degenerate mobility cases in a quasistatic setting.

Contribution

It introduces a novel finite-strain poro-visco-elastic model with degenerate mobility and proves the existence of weak solutions using energy-dissipation inequalities.

Findings

Existence of weak solutions for the nonlinear model.

Handling of degenerate mobility in the model.

Application of energy-dissipation inequalities for proof.

Abstract

A quasistatic nonlinear model for poro-visco-elastic solids at finite strains is considered in the Lagrangian frame using the concept of second-order nonsimple materials. The elastic stresses satisfy static frame-indifference, while the viscous stresses satisfy dynamic frame-indifference. The mechanical equation is coupled to a diffusion equation for a solvent or fluid content. The latter is pulled-back to the reference configuration. To treat the nonlinear dependence of the mobility tensor on the deformation gradient, the result by Healey & Kr\"omer is used to show that the determinant of the deformation gradient is bounded away from zero. Moreover, the focus is on the physically relevant case of degenerate mobilities. The existence of weak solutions is shown using a staggered time-incremental scheme and suitable energy-dissipation inequalities.