M. Goldbart'
- Xiangjun Xing
- Annette Zippelius
title: Soft random solids and their heterogeneous elasticity
---

Introduction {#SEC:Intr}
============

Random solids, such as chemical gels, rubber, glasses and amorphous silica, are characterized by their [*structural*]{} heterogeneity, which results from the randomness locked-in at the time they are synthesized. The mean positions of the constituent particles exhibit no long-range order, and every particle inhabits a unique spatial environment. The [*elasticity*]{} of random solids also inherits heterogeneity from this locked-in randomness. For example, the Lamé coefficients and the residual stress vary from point to point throughout the elastic medium. The central goal of this paper is to develop a statistical characterization of random elastic media, via the mean values of the Lamé coefficients and the residual stress as well as the two-point spatial correlations amongst the fluctuations of these quantities, which we shall name as the disorder correlator. These mean values and correlations are to be thought of as averages taken over realizations of the sample fabrication for a given set of fabrication parameters. We expect these characteristic quantities to coincide with the volume-averages of their single-sample counterparts.

Our focus will be on [*soft*]{} random solids. These are network media that 