A multi-axial, multimechanism based constitutive model for the comprehensive representation of the evolutionary response of SMAs under general thermomechanical loading conditions

We present a fully general, three dimensional, constitutive model for Shape Memory Alloys (SMAs), aimed at describing all of the salient features of SMA evolutionary response under complex thermomechanical loading conditions. In this, we utilize the mathematical formulation we have constructed, along with a single set of the model’s material parameters, to demonstrate the capturing of numerous responses that are experimentally observed in the available SMA literature. This includes uniaxial, multi-axial, proportional, non-proportional, monotonic, cyclic, as well as other complex thermomechanical loading conditions, in conjunction with a wide range of temperature variations. The success of the presented model is mainly attributed to the following two main factors. First, we use multiple inelastic mechanisms to organize the exchange between the energy stored and energy dissipated during the deformation history. Second, we adhere strictly to the well established mathematical and thermodynamical requirements of convexity, associativity, normality, etc. in formulating the evolution equations governing the model behavior, written in terms of the generalized internal stress/strain tensorial variables associated with the individual inelastic mechanisms. This has led to two important advantages: (a) it directly enabled us to obtain the limiting/critical transformation surfaces in the spaces of both stress and strain, as importantly required in capturing SMA behavior; (b) as a byproduct, this also led, naturally, to the exhibition of the apparent deviation from normality, when the transformation strain rate vectors are plotted together with the surfaces in the space of external/global stresses, that has been demonstrated in some recent multi-axial, non-proportional experiments.