Mathematical model for superelastic shape memory alloy springs with large spring index

Abstract A new model is proposed for the behavior of superelastic shape memory alloy (SMA) helical springs with large index. The derived governing equations consider the response of the spring to monotonic loading followed by complete unloading. In particular, the relation between axial force and axial deformation and the distribution of shear stress in a cross section of the spring wire are determined analytically for the entire loading-unloading cycle. Special attention is given to modeling the unloading stage, for which the proposed solution improves upon existing literature. The model is validated by comparison to 3D finite element simulations and the governing equations are used to investigate the influence of temperature, wire radius and mean radius on the superelastic behavior of a sample SMA spring.