This project is focused on systematic experimental investigation and theoretical description of nucleation and propagation of martensitic phase transformation via localized inhomogeneities in NiTi shape memory alloys, so-called transformation bands. The localization phenomenon strongly influences mechanical behaviors of these alloys and plays key role in understanding other material processes as transformation-induced plasticity or functional fatigue. Microstructural origins of the phenomenon will be investigated both experimentally – e.g. grain-by-grain mapping of stress and strain with advanced 3D XRD method – and through mathematical models. Based on the results, a macroscopic, mathematically and thermodynamically consistent nonlocal constitutive model will be formulated and implemented into a numerical software, which allows predictions of localization in practical applications. This project further elaborates and expands recent activities of the research team recognized and appreciated by the scientific community.