On the modeling of thermo-mechanical phase transformations in solids

The present paper represents an effort to model coupled thero-mechanical effects in the mcroscopic response of solids that arise from the occurrence of phase transformations. A Helmholtz free energy potential is constructed to describe the response of the thermoelastic material to be considered. Apart from some considerations pertaining to properties of the hypothetical material, the analysis is carried out in the context of a simple problem, idealized from an experiment, in which an annular cylinder is deformed to a state of radially symmetric, finite anti-plane shear in the presence of differing inner and outer surface temperatures. After constructing all radially symmetric weak solutions involving at most a single surface of discontinuity of strain or temperature gradient, we determine the implications for quasi-static motions of the second law of thermodynamics. In particular, the results concerning creep as predicted by the present model are in qualitative agreement with the results of the motivating experiment.