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 essentially one-dimensional, 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 based on thermodynamic principles. 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 analyzed in relation to experimental evidence available in the literature. In particular, the influence of the strain rate and of the ambient conditions on the response of the model is highlighted.