A nonlinear mesoscopic elastic class of materials

It is becoming clear that the elastic properties of rock are shared by numerous other materials (sand, soil, some ceramics, concrete, etc.). These materials have one or more of the following properties in common: strong nonlinearity, hysteresis in stress–strain relation, and discrete memory. Primarily, it is the material’s compliance, the mesoscopic linkages between the rigid components, that give these materials their unusual elastic properties. It can be said that these materials have nonlinear mesoscopic elasticity and encompass a broad class of materials. Materials with nonlinear mesoscopic elasticity stand in contrast to liquids and crystalline solids whose elasticity is due to contributions of atomic level forces, i.e., materials with atomic elasticity. Atomic elastic materials are well described by the traditional (Landau) theory of elasticity; however, mesoscopic elastic materials are not. Mesoscopic materials are well described by the P-M (Preisach–Mayergoyz) model of nonlinear elasticity developed by Guyer and McCall. A sequence of experiments on numerous materials illustrate the evidence of nonlinear mesoscopic elastic behavior. In experimental analysis a surprising discovery was made: damaged atomic elastic materials behave as mesoscopic elastic materials. It is significant that the nonlinear mechanism(s) in mesoscopic elastic materials remains a mystery.