A New Constitutive Modeling Approach for Shape Memory Alloys

A new thermomechanical constitutive modeling approach for shape memory alloys (SMAs) that undergo a martensite to austenite phase transformation and the associated pseudoelastic and shape memory responses is presented. The novelty of this new formulation is that a single transformation surface is implemented in order to capture the forward and reverse phase transformations, as well as the reorientation and detwinning of the martensite phase. The framework is akin to the usual flow theory plasticity with kinematic hardening, however in addition to the transformation strain there is also a transformation entropy that is directly related to the martensite volume fraction appearing in prior theories. A transformation surface in effective stress and effective temperature space is introduced and an associated flow rule governs the evolution of the transformation strain and entropy. In order to capture the multitude of SMA behaviors, a transformation potential function is introduced in transformation strain and entropy space for the derivation of the back stresses and back temperatures that define the kinematic hardening behavior. It is this potential function that governs all of the important behaviors within the model. After the description of the general theory, specific forms for the transformation surface and the transformation potential are devised and results for the behaviors captured by the model are provided for a range of thermomechanical loadings. The model is then implemented in finite element calculations to investigate the structural response of shape memory alloy tubes, bars, and beams.