A phase-field model for shape memory alloys at macroscopic scale: uni-axial deformation tests under different control conditions

We propose a model for the thermomechanical behaviour of a shape memory alloy based on a phase-eld approach to the underlying martensitic phase transition. The model is applied at the macroscopic scale and it is formulated to capture essentially the one-dimensional mechanical behaviour; in fact, the eect of the martensitic phase transition has been included in terms of a uni-axial deformation along a xed direction. In addition to the usual momentum balance equation, a time-dependent Ginzburg-Landau equation is introduced to describe the evolution of the phase; a central constitutive relation couples the phase to the deformation. Finally, the heat equation accounts for the non isothermal effects due to the phase transformation in a thermodynamically consistent way. The model has been implemented within a nite-element framework and the mechanical response of the model under dierent conditions is investigated in a number of numerical tests; the results obtained are analysed and compared to experimental evidences available in literature.