Flow and deformation due to periodic loading in a soft porous material

TL;DR

This paper investigates how periodic loading affects flow and deformation in soft porous materials using a 1D poroelastic model, revealing distinct regimes and nonlinear effects relevant to biological tissues and soils.

Contribution

It provides a systematic analysis of the parameter space for periodic deformations, including analytical solutions and numerical exploration of nonlinear effects and localization phenomena.

Findings

Two mechanical regimes identified based on loading period

Analytical solutions for slow loading and small amplitude cases

Large deformations cause asymmetry in porosity and fluid flux

Abstract

Soft porous materials, such as biological tissues and soils, are exposed to periodic deformations in a variety of natural and industrial contexts. The detailed flow and mechanics of these deformations have not yet been systematically investigated. Here, we fill this gap by identifying and exploring the complete parameter space associated with periodic deformations in the context of a 1D model problem. We use large-deformation poroelasticity to consider a wide range of loading periods and amplitudes. We identify two distinct mechanical regimes, distinguished by whether the loading period is slow or fast relative to the characteristic poroelastic timescale. We develop analytical solutions for slow loading at any amplitude and for infinitesimal amplitude at any period. We use these analytical solutions and a full numerical solution to explore the localisation of the deformation near the permeable boundary as the period decreases and the emergence of nonlinear effects as the amplitude increases. We show that large deformations lead to asymmetry between the loading and unloading phases of each cycle in terms of the distributions of porosity and fluid flux.