Generic Stress Rectification in Nonlinear Elastic Media

TL;DR

This paper demonstrates that nonlinear elastic media inherently rectify anisotropic internal stresses towards contraction or expansion depending on their properties, with implications for biological and granular materials.

Contribution

The study provides a general theoretical framework showing how different nonlinear elastic media rectify internal stresses, extending understanding beyond fiber networks.

Findings

Bucklable and linear materials rectify small forces towards contraction.

Granular-like materials rectify forces towards expansion.

Results extend to larger forces and other material types.

Abstract

Stress propagation in nonlinear media is crucial in cell biology, where molecular motors exert anisotropic force dipoles on the fibrous cytoskeleton. While the force dipoles can be either contractile or expansile, a medium made of fibers which buckle under compression rectifies these stresses towards a biologically crucial contraction. A general understanding of this rectification phenomenon as a function of the medium's elasticity is however lacking. Here we use theoretical continuum elasticity to show that rectification is actually a very general effect in nonlinear materials subjected to anisotropic internal stresses. We analytically show that both bucklable and constitutively linear materials subjected to geometrical nonlinearities rectify small forces towards contraction, while granular-like materials rectify towards expansion. Using simulations, we moreover show that these results extend to larger forces. Beyond fiber networks, these results could shed light on the propagation of stresses in brittle or granular materials following a local plastic rearrangement.