A Mathematical Formulation for Rate Independent Martensitic Phase Transformations

The evolution of a single phase boundary which is hindered by dry friction can be described by a variational inequality and a rate law. The idea is to obtain existence of generalized solutions by extending the problem from pure phase distributions to phase mixtures. To relate the extended problem to the original problem a generalized relaxation concept for general rate independent evolution problems is presented. In a simple case it is possible to apply the abstract concept to a special phase transformation problem, i.e. a mathematical rigorous derivation of a coarse grained model can be established.