Comparative analysis of numerical methods for constitutive modeling of shape memory alloys

Abstract

Abstract This article presents a comparative analysis of four numerical approaches—Newton Raphson method, trust region dogleg method, implicit solver (IS) based method considering a proposed simplified differential phase kinetics as well as an existing arbitrary loading based phase kinetics to solve the constitutive equation of shape memory alloy (SMA). These numerical methods can be applied to model any SMA-based actuator under thermo-mechanical loading. To demonstrate these methods, a configuration of SMA wire with a normal bias spring is considered as a case study, and its mathematical model is solved with the above-mentioned numerical approaches. Further, a comparative study is carried out that compares the solutions obtained via these methods and with the published literature. It highlights the numerical stability, computational time, and the level of complexity for the implementation of the numerical methods. The study details out both the merits and demerits of the presented numerical methods and the computational algorithms to implement these methods. Among the discussed methods, it is concluded that the IS-based numerical method with the proposed differential form of Chung’s phase kinetics model seems better for implementing the constitutive modeling for the selected case study.