Surface instability of sheared soft tissues

TL;DR

This paper investigates how surface instability in soft tissues under shear is influenced by collagen fibers, showing that fiber orientation and stiffness significantly affect the onset of wrinkling, unlike in elastomers.

Contribution

It introduces a model incorporating collagen fibers into nonlinear elasticity to analyze their effect on surface instability under shear in soft tissues.

Findings

Neo-Hookean model predicts instability only at very high shear.

Fiber orientation and stiffness ratio E/mu critically influence stability.

Surface instability is more likely when shear is against fiber direction.

Abstract

When a block made of an elastomer is subjected to large shear, its surface remains flat. When a block of biological soft tissue is subjected to large shear, it is likely that its surface in the plane of shear will buckle (apparition of wrinkles). One factor that distinguishes soft tissues from rubber-like solids is the presence -- sometimes visible to the naked eye -- of oriented collagen fibre bundles, which are stiffer than the elastin matrix into which they are embedded but are nonetheless flexible and extensible. Here we show that the simplest model of isotropic nonlinear elasticity, namely the incompressible neo-Hookean model, suffers surface instability in shear only at tremendous amounts of shear, i.e., above 3.09, which corresponds to a 72 degrees angle of shear. Next we incorporate a family of parallel fibres in the model and show that the resulting solid can be either reinforced or strongly weakened with respect to surface instability, depending on the angle between the fibres and the direction of shear, and depending on the ratio E/mu between the stiffness of the fibres and that of the matrix. For this ratio we use values compatible with experimental data on soft tissues. Broadly speaking, we find that the surface becomes rapidly unstable when the shear takes place "against" the fibres, and that as E/mu increases, so does the sector of angles where early instability is expected to occur.