A non-isothermal phase-field model for shape memory alloys: Numerical simulations of superelasticity and shape memory effect under stress-controlled conditions

A phase-field–based model has been employed for numerical tests on the mechanical response of a shape memory alloy. The model consists of a time-dependent Ginzburg–Landau equation for a scalar order parameter describing the local phase of the material (austenite or martensite), coupled with the balance of linear momentum and the heat equations; the mechanical effect of the martensitic phase transition is described in terms of a uniaxial deformation strain along a fixed direction, making the model suited for predictions over monodimensional specimens. A number of numerical simulations under stress-controlled conditions have been performed to investigate the mechanical behaviour of the model; the results obtained are analysed in relation to the experimental evidences available in the literature and previous investigations under strain-controlled conditions.