A solid-fluid mixture model allowing for solid dilatation under external pressure

TL;DR

This paper introduces a new solid-fluid mixture model that captures the dilatational behavior of porous materials under external pressure, explaining volume expansion without density change.

Contribution

The model uniquely accounts for solid dilatation under pressure using the Principle of Virtual Power and simple free energy dependence, addressing a gap in existing theories.

Findings

Model successfully describes solid dilatation behavior

Captures volume increase with constant density under pressure

Provides a simplified framework for porous material analysis

Abstract

A sponge subjected to an increase of the outside fluid pressure expands its volume but nearly mantains its true density and thus gives way to an increase of the interstitial volume. This behaviour, not yet properly described by solid-fluid mixture theories, is studied here by using the Principle of Virtual Power with the most simple dependence of the free energy as a function of the partial apparent densities of the solid and the fluid. The model is capable of accounting for the above mentioned dilatational behaviour, but in order to isolate its essential features more clearly we compromise on the other aspects of deformation.