A macroscale, phase-field model for shape memory alloys with non-isothermal effects: influence of strain-rate and environmental conditions on the mechanical response

A Ginzburg-Landau model for the macroscopic behaviour of a shape memory alloy is proposed. The model is one-dimensional in essence, in that we consider the effect of the martensitic phase transition in terms of a uniaxial deformation along a fixed direction and we use a scalar order parameter whose equilibrium values describe the austenitic phase and the two martensitic variants. The model relies on a Ginzburg-Landau free energy defined as a function of macroscopically measurable quantities, and accounts for thermal effects; couplings between the various relevant physical aspects are established according to thermodynamic consistency. The theoretical model has been implemented within a finite-element framework and a number of numerical tests are presented which investigate the mechanical behaviour of the model under different conditions; the results obtained are analysed in relation to experimental evidences available in literature. In particular, the influence of the strain-rate and of the ambient conditions on the response of the model is highlighted.