Elastic heterogeneity of soft random solids

TL;DR

This paper investigates the spatial heterogeneity of elastic properties in soft random solids using phenomenological and semi-microscopic models, revealing long-range correlations and universal parameters affecting residual stress and shear modulus.

Contribution

It introduces a connection between phenomenological and semi-microscopic models, elucidating the statistical properties and correlations of elastic heterogeneity in soft random solids.

Findings

Residual stress correlations are long-ranged.

A universal parameter governs residual stress and shear modulus.

Goldstone fluctuations reproduce phenomenological model predictions.

Abstract

Spatial heterogeneity in the elastic properties of soft random solids is investigated via a two-pronged approach. First, a nonlocal phenomenological model for the elastic free energy is examined. This features a quenched random kernel, which induces randomness in the residual stress and Lame coefficients. Second, a semi-microscopic model network is explored using replica statistical mechanics. The Goldstone fluctuations of the semi-microscopic model are shown to reproduce the phenomenological model, and via this correspondence the statistical properties of the residual stress and Lame coefficients are inferred. Correlations involving the residual stress are found to be long-ranged and governed by a universal parameter that also gives the mean shear modulus.