Extension of a Linear Behaviour Model of Shape Memory Alloys for Finite Strain Studies

Abstract
Within a thermodynamical approach associated to the classical local state postulate, a constitutive macroscopic model, named R_L model [1][2], has been built in order to predict the pseudoelastic behaviour of shape memory alloys (SMA). This behaviour occurs with a martensitic transformation. The volume fraction of martensite z is taken as internal variable and the evolution kinetics of z are derived from metallurgical considerations. In its existing form, the R_L model is only valid for small strain calculations. In this paper, an extension is proposed for finite tranformations. Using a formulation in a rotating frame, the obtained model is closed form of the original one. For numerical calculations of NiTi thin films, a stress computation algorithm is also presented. It consists on two steps, the first one is an elastic prediction and the second, a possible pseudoelastic correction. The correction follows an implicit Euler-backward method. To ensure the convergence of the Newton scheme for FE simulation, a consistent tangent operator is used. The results obtained with the proposed approach are in good agreement with the experiments.