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. •A constitutive model is constructed involving phase transformation in 1D SMA.•The model includes the coupling effect between thermal and mechanical fields.•The proposed model takes the tension–compression asymmetry into account.•3D deformation of the crystalline lattice is analyzed.•An asymmetric potential energy function is constructed.•The proposed model can capture the asymmetric phase transformation.•The proposed model can capture the characteristics of SMA in tension and compression•Both single-crystalline model and poly-crystalline model are proposed.•The proposed model is simple but high-precision compared with the existing models.