Deformation of Shape Memory Alloys Due to Thermo-Induced Transformation

In this paper, a macro-scale, phenomenological constitutive model for shape memory alloys is used in conjunction with energy balance equations to study the evolution of temperature and deformation profiles seen in SMA wires under specific thermal and mechanical boundary conditions. The general, fully coupled thermo-mechanical problem is formulated and analytical solutions are determined for the decoupled case and limit cases. Results for two specific initial/boundarv value problems are presented here: 1) resistive heating of an SMA wire-initial detwinned martensite leads to strain recovery (contraction) on heating; 2) deformation wave in a semiinfinite, initially austenitic SMA wire cooled at the boundary-deformation zone propagates and expands as the wire transforms to martensite (expansion). In both cases, the region and extent of transformation is identified, indicating the magnitude of actuation obtained. Implications of the modeling for the active control of structures are discussed.