Several years ago, the use of shape memory alloys (SMA) in industrial applications gained a real interest. Even if SMA suppliers can produce a wide variety of materials, the elaboration of efficient and optimized applications remains quite hazardous due to the lack of computer-aided design tools. To fill this gap, a new phenomenological material law based on kriging was recently developed. From a single formulation constructed with isothermal tensile curves, the model calculates the thermomechanical behavior of SMA including superelasticity, one-way and assisted two-way shape memory effects among others. The paper presents the concepts that are used to generalize the model from a uniaxial to a tensorial formulation. Equivalent values defined from a Prager criterion are adapted from plasticity. Numerical results are validated by a series of experimental curves obtained with SMA samples for different loading conditions. The generalized material law is intended to be implemented with finite elements in order to calculate the thermomechanical behavior of complex shape memory devices.
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