A projected Newton algorithm for simulation of multi-variant textured polycrystalline shape memory alloys

The unique behavior of shape memory alloys derives from its ability of phase transformation instead of slip. A reason for the phase transformation is the microstructural occurrence and amount of different variants for the multi-variant- and detwinned-martensite dependent on the stress state as well as preferred directions in textured materials. The model presented in this paper enables to take into account all martensitic variants in different orientated grains. The main focus of this paper is the numerical implementation of a known, but advanced model with a projected Newton algorithm and a residual including only two vectors of unknowns. Additionally the texture of a pseudoelastic NiTi wire is measured and the orientations and their weight/size are implemented. Finally in a finite element example the superelastic behavior of a stent with different stress states at different locations is investigated.