A modified Landau phenomenological constitutive model for the tension-compression asymmetry in one-dimensional Shape Memory Alloys

Shape Memory Alloys (SMA) have unique properties because of their unique ability to reversibly transform when subjected to appropriate thermal and/or mechanical loads. A phenomenological constitutive model is constructed involving phase transformation in one-dimensional SMA. The model is based on the Landau theory and includes the coupling effect between thermal and mechanical fields. Taking into account the tension?compression asymmetry, an asymmetric potential energy function is constructed, according to the three-dimensional deformation of the crystalline lattice. Both single-crystalline model and poly-crystalline model are proposed, and the angle between the lattice plane and the force (deformation) direction is considered in the poly-crystalline model. Numerical experiments have been carried out, which can well capture the asymmetric phase transformation and tension?compression asymmetry.