Simulation of asymmetric effects for shape memory alloys by decomposition of transformation strains

Experimental results of shape memory alloys show different characteristic material effects dependent on the stress state such as tension, compression and shear. A microstructural reason for these asymmetric effects is the occurrence of different variants for the multi-variant- and detwinned-martensite dependent on the stress state. For simulation, a decomposition of the transformation strain tensor into individual quantities is introduced. These are related to certain stress states, which are characterized in the octahedral plane of the deviatoric stress space in terms of the Lode angle. This enables an additive decomposition of the yield function as a sum of weighted stress mode related quantities. Furthermore a flow rule is formulated in the framework of plasticity. Additionally, thermodynamic consistency of the constitutive equations is shown for two different prototype models and verification of the proposed approach is succeeded to simulate the pseudoelastic behaviour of two different NiTi shape memory alloys with different hardening behaviour dependent on the stress state. In a finite element example the superelastic behaviour of a stent with different stress states at different locations is investigated.