Simulation of thermomechanical behavior of shape-memory alloys under multiaxial non-proportional stress

The paper presents a mathematical description of polycrystalline shape memo ry alloys within the framework of continuum mechanism where the spatially m ultidimensional case is considered. A new simple model is introduced, which correctly describes not only all well-studied shape memory effects (e.g. o ne-way-effect, pseudo-elasticity) but also the more complex behavior (e.g. reorientation of stress-induced martensite). The key idea is a new set of i nternal state variables, which are averaged values for a representative vol ume element of the polycrystalline material. A tensor-valued variable (tran sformation strain tensor) describes the state of orientation of martensite. The relative volume fraction of stress induced martensite is defined by ch oosing a certain tensor norm of this internal variable.