Mesoscopic free energy as a framework for modeling shape memory alloys

This article presents a reinterpretation of the one-dimensional shape memory alloy model by Müller, Achenbach, and Seelecke (M-A-S) that offers extended capabilities and a simpler formulation. The cornerstone of this model is a continuous, multi-well free energy that governs phase change at a mesoscopic material scale. The free energy has been reformulated to allow asymmetric tensile and compressive behavior as well as temperature-dependent hysteresis while maintaining the necessary smoothness conditions. The free energy is then used to derive expressions for latent heat coefficients that include the influence of stress, the difference in stiffness between the phases, and irreversibility. Special attention is devoted to the role of irreversibility and latent heat predictions, which are compared to experimental measurements. The new model also includes an updated set of kinetics equations that operate on the convexity of the energy wells instead of the height of the energy barriers. This modification eliminates several sets of equations from the overall formulation without any compromises in performance and also bypasses limitations of the barrier-based equations.