Coupled normal-shear stress models for SMA response

In the present paper two constitutive models, able to reproduce the mechanical behavior of shape memory alloy (SMA), are proposed. The constitutive laws allow considering the simultaneous presence of normal and shear stresses, accounting for its coupling without developing a full three-dimensional (3D) model. In such a way, two different models suitable for deriving the response of SMA devices, both characterized by the presence of only normal and shear stresses, are presented. In particular, the proposed SMA models reproduce the pseudoelastic behavior, the shape memory effect, the reorientation process and account for the different elastic properties of austenite and martensite. The phase transformations are governed by an equivalent stress defined as function of the normal and shear stresses. A robust numerical algorithm, based on a backward Euler time integration within a predictor-corrector technique, is developed for each model. Numerical simulations of experimental evidences, available in literature, are performed to validate the proposed models and computational strategies. In particular, comparisons of the results obtained by the proposed models with experimental data, are performed. A comparison with a 3D model is also carried out. The ability of the proposed models in satisfactorily reproducing the SMA response with reduced computational cost is verified even for complex loading-unloading histories.