Global Existence for a Second-Order Thermo-Mechanical Model of Shape MemoryAlloys

摘要

A thermo-mechanical model of structural phase transitions in solids isconsidered. In this model the free energy depends on temperature, macroscopic deformation and also on the proportions of the phases. The related initial-boundary value problem consists of equilibrium equations for energy and momentum coupled with an evolution variational inequality for the phase proportions. Fourth-order regularizing terms are neglected in the momentum balance equation. Using an approximation-a priori estimates-passage to the limit procedure we show the existence of a solution in any dimension of space.