A shape memory alloy model by a second order phase transition

• we suggest for shape memory alloys a phase field model by a second order phase transition.
• We obtain a simulation of phase dynamics convenient to describe the behavior of these materials.
• The use of this new model is characterized: by new potentials of the Ginzburg–Landau equation; by new dependence on the temperature in the constitutive equation.
• We obtain simulations in better agreement with experimental data.

Motivated by the experimental results of the paper [1] and unlike the general theories of shape memory alloys (SMAs), in this paper we suggest for such materials a phase field model by a second order phase transition. So that, with this new system we obtain a simulation of phase dynamics very convenient to describe the natural behavior of these materials. The differential system is governed by the motion equation, the heat equation and the Ginzburg–Landau (GL) equation and by a constitutive law between the phase field, the temperature, the strain and the stress. The use of this new model is characterized by new potentials of the GL equation and by a new dependence on the temperature in the constitutive equation. Using this new model, we obtain simulations in better agreement with experimental data and respect to previous work [2].