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.