A phase-space formulation of existence and relaxation theory in elasticity

We discuss a formulation of elasticity in which compatibility and equilibrium equations are separated from the material law relating stresses and strains, resulting in a model defined on the space of strain-stress field pairs, or phase space. The problem consists of minimizing the distance between a given material data set and the subspace of compatible strain fields and stress fields in equilibrium. We find that the classical solutions are recovered in the case of linear elasticity and for some examples in nonlinear elasticity.

We develop a corresponding concept of relaxation, which turns out to be fundamentally different from the classical relaxation of energy functions. This talk is based on joint work with Stefan Müller and Michael Ortiz.