Scaling laws for the response of nonlinear elastic media with implications for cell mechanics

TL;DR

This paper investigates how nonlinear elasticity, especially strain stiffening, influences the response of elastic media to internal forces, revealing scaling laws that connect local forces to far-field strains, with implications for cell mechanics.

Contribution

It introduces scaling laws for nonlinear elastic responses to internal forces, highlighting how strain stiffening alters the spatial distribution of stresses in materials like biological tissues.

Findings

Strain stiffening causes sign changes in strains with distance from force sources.

Scaling laws with irrational exponents relate near-field and far-field strains.

Radial compression occurs around contractile inclusions or molecular motors.

Abstract

We show how strain stiffening affects the elastic response to internal forces, caused either by material defects and inhomogeneities or by active forces that molecular motors generate in living cells. For a spherical force dipole in a material with a strongly nonlinear strain energy density, strains change sign with distance, indicating that even around a contractile inclusion or molecular motor there is radial compression; it is only at long distance that one recovers the linear response in which the medium is radially stretched. Scaling laws with irrational exponents relate the far-field renormalized strain to the near-field strain applied by the inclusion or active force.