Theoretical and numerical modeling of shape memory alloys accounting for multiple phase transformations and martensite reorientation

•Development of a generalized 3D phenomenological constitutive model for SMAs.•Martensite reorientation, multiple phase transitions and secondary effects included.•Numerical implementation based on Fischer–Burmeister complementary function.•Numerical simulations in good agreement with experimental results.•Assessment of the proposed model and of the numerical procedure efficiency for complex FE analysis.

The present paper develops a refined and general three-dimensional phenomenological constitutive model for shape memory alloys (SMAs), along the lines of what recently proposed by Auricchio and Bonetti (2013) in a more theoretical context. Such an improved model takes into account several physical phenomena, as martensite reorientation and different kinetics between forward/reverse phase transformations, including also smooth thermo-mechanical response, low-stress phase transformations as well as transformation-dependent elastic properties. The model is treated numerically through an effective and efficient procedure, consisting in the replacement of the classical set of Kuhn–Tucker inequality conditions by the so-called Fischer–Burmeister complementarity function. Numerical predictions are compared with experimental results and the finite element analysis of a SMA-based real device is described to assess the reliability of the proposed model as well as the effectiveness of its numerical counterpart.