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 charac...