Dynamics of poroelastic filaments

TL;DR

This paper develops a mathematical model called poroelastica to study the stability and nonlinear dynamics of slender poroelastic rods, incorporating fluid-solid interactions, with applications to biological and soft materials.

Contribution

It introduces the poroelastica equation, extending elastic rod theory to include fluid effects, and analyzes buckling and instability phenomena in poroelastic filaments.

Findings

Derived the poroelastica evolution equation including fluid-solid interaction terms.

Analyzed buckling and instability under various load and boundary conditions.

Applied the model to biological and soft material structures.

Abstract

We investigate the stability and geometrically non-linear dynamics of slender rods made of a linear isotropic poroelastic material. Dimensional reduction leads to the evolution equation for the shape of the poroelastica where, in addition to the usual terms for the bending of an elastic rod, we find a term that arises from fluid-solid interaction. Using the poroelastica equation as a starting point, we consider the load controlled and displacement controlled planar buckling of a slender rod, as well as the closely related instabilities of a rod subject to twisting moments and compression when embedded in an elastic medium. This work has applications to the active and passive mechanics of thin filaments and sheets made from gels, plant organs such as stems, roots and leaves, sponges, cartilage layers and bones.