A Constitutive Model of Shape Memory Alloys Based on Viscoplastic like Evolution Equations

The paper presents a new model that allows the simulation of the macroscopic thermomechanical behavior of shape memory alloys (SMA). In this paper we present a description of the austenite-martensite phase transition, which takes into account the two types of martensite by introducing suitable internal variables: the volume fractions of the self-accommodating product phase (pure thermal effect) and the oriented (stress induced) product phase. The evolution equations of the internal variables are similar to the evolution equation in viscoplasticity. Differing from previous models, the presented one is able to model the behaviour of the SMA under combined thermal and mechanical loads. A numerical example is given that illustrates the ability of the model to capture the thermomechanical behavior of shape memory alloys under temperature change and proportional loadings