Heterogeneous Solids and the Micro/macro Connection: Structure and Elasticity in Architecturally Complex Media as Emergent Collective Phenomena

Launched before the atomic hypothesis took hold, elasticity theory is a spectacular achievement. A continuum-level description, it provides a powerful toolkit for determining how architecturally simple solids such as crystals respond macroscopically to stress, whilst encoding microscopic, atomic-realm details parsimoniously, via a few parameters. Solids that are architecturally complex at the atomic level—such as vulcanized rubber, gels and glasses—are commonly addressed using elasticity theory, too. However, their microscopic-level irregularity raises new issues, not only of elasticity but also of structure: How do the elastic ‘constants’ of such media fluctuate across a sample? Do such media strain non-affinely in response to stresses? Are there regional variations in the position-fluctuations of the atoms? More generally, can the structure and elasticity of architecturally complex solids be viewed as emergent collective phenomena, determinable from their underlying microscopic thermal motion and characterizable by some suitable continuum theory?