Macroscopic equilibrium domain structure and geometric compatibility in elastic phase transition of thin plates

Different macroscopic domain structures have been observed during stress-induced austenite to martensite phase transition in thin plates of NiTi polycrystalline shape memory alloy (SMA) under quasi-static tension. This paper studies the role of geometric compatibility in forming two-dimensional (2D) equilibrium domain structures in plates of different aspect ratios W/L (width/length). A nonconvex and nonlocal continuum model of the material is developed and implemented into a finite-element code to simulate the formation of macroscopic domain structures during isothermal quasi-static displacement-controlled stretching of the plates. It is shown that geometric compatibility between the deformation of the domains and the boundary constraints plays a key role in the formation of domain structures. As the degree of boundary constraint is increased by an increase in the width/length ratio W/L of the plate, the equilibrium domain structure changes from the single domain to multiple domains and eventually to martensite-twin domains. At the same time, stress-strain responses in transforming the plates change with W/L. The main results of our modeling agree qualitatively with experimental observations.