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.Comment: 5 page
