Existence Result for a Thermo-Mechanical Model of Shape Memory Alloys

摘要

The paper is concerned with a mathematical study of the Fremond thermo-mechanicalmodel for structural phase transitions in solids. In order to take shape memory effects into account, the free energy is assumed to depend on the local proportions of the phases in addition to temperature, macroscopic strain, and strain gradient. The corresponding equilibrium equations consist of the balance laws of momentum and energy coupled with an evolution variational inequality for the phase proportions. Regarding the resulting initial-boundary value problem, the review of previous papers shows that the related mathematical results refer to the quasi static situation. On the contrary, here the authors keep the inertial term in the momentum balance equation. By applying an approximation--a priori estimates--passage to the limit procedure the authors prove the existence of a weak solution of the problem in any dimension of space.