In this paper, the pure torsion of SMA curved bars with circular cross sections is studied analytically. First, a three-dimensional phenomenological macroscopic constitutive model for polycrystalline SMAs is reduced to the one-dimensional pure shear case and then a closed-form solution for torsional response of SMA curved bars in loading and unloading is obtained. The effect of a direct shear force in the cross section is also considered in the solution which enables the formulation for analyzing SMA helical springs. Several case studies are presented in order to investigate the accuracy of the proposed method in predicting the torsional response of SMA curved bars, the stress distributions, and analyzing SMA helical springs.

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