Elasticity of Inhomogeneous materials: relaxing the affine assumption.

Brian DiDonna, IMA

There has recently been a surge of interest in the rheology of inhomogenous materials such as foams, granular materials, and biopolymer networks. The elastic response of such materials is strongly affected by non-uniformities in the displacement field at intermediate length scales. I will present a general framework for the non-uniform, or "non-affine" component of a material's response to externally applied stresses. This framework succeeds in separating the microscopic elasticity of material sub-blocks from macroscopic structural effects.