Geometry of Needle-Like Microstructures in Shape-Memory Alloys

Abstract Needle-like microstructures are often observed in shape memory alloys near macro-interfaces that separate regions with different laminate orientation. We study their a two-dimensional model based on nonlinear elasticity, contains an explicit parametrization of the needle profiles. Energy minimization leads to specific predictions for geometry needle-like domains. Our simulations optimization interfaces, using polyconvex energy density cubic symmetry elastic problem, and numerical implementation via finite elements dynamically changing grid.