Theoretical and numerical modeling of solid–solid phase change: Application to the description of the thermomechanical behavior of shape memory alloys

The mechanical behavior of a solid capable of undergoing internal phase change is considered. Reversible and dissipative constitutive equations are established within the framework of generalized standard materials with internal constraints. These constraints are accounted for using Lagrange multipliers. The presented model is based upon a phenomenological configuration in series (Reuss model). In the case of reversible phase change, it is shown that the elastic energy of the material can be obtained by convexifying the energy functions of existing phases. In the dissipative case, it is shown how the behavior of the material can be made stable by developing evolution equations deriving from an adequately chosen dissipation potential. As an application, we propose a description of the thermomechanical behavior of shape memory alloys (SMAs). The obtained constitutive equations can be used to simulate the pseudoelastic response of SMAs as well as the one-way shape memory effect. Validation against experimental data is performed in the case of multi-axial complex thermomechanical loading for NiTi as well as Cu-based alloys.