Nonlocal elasticity near jamming

TL;DR

This paper reveals that the elasticity of jammed solids exhibits nonlocal behavior, with multiple diverging length scales influencing their response, leading to improved constitutive models for materials like emulsions and foams.

Contribution

It provides direct measurements of nonlocal elastic responses in jammed solids and identifies multiple diverging length scales controlling these effects.

Findings

Elasticity in jammed solids is nonlocal.

Three distinct length scales influence nonlocal effects.

New constitutive relations improve modeling of weakly jammed materials.

Abstract

We demonstrate that the elasticity of jammed solids is nonlocal. By forcing frictionless soft sphere packings at varying wavelength, we directly access their transverse and longitudinal compliances without resorting to curve fitting. The observed wavelength dependence of the compliances is incompatible with classical (local) elasticity, and hence quantifies the amplitude of nonlocal effects. Three distinct length scales, two of which diverge, control the amplitude of both nonlocal effects and fluctuations about the mean response. Our results identify new, more accurate constitutive relations for weakly jammed solids, including emulsions, foams, and granulates.