Two variant thermomechanical model for shape memory alloys

A thermomechanical model is proposed to predict the shape memory and superelastic behaviors in two variant shape memory alloys (SMA). The model is based on two internal variables which are the phase fractions of the variants of martensite. The evolution of these internal variables as functions of the stress, strain and temperature loading history is described geometrically in phase space and by differential equations of the Duhem-Madelung form. For any specified constant ratio of the variants of martensite, the model reduces to a one variant thermomechanical model similar to the Ivshin-Pence model.