Exact solutions for pure torsion of shape memory alloy circular bars

Shape memory alloy (SMA) structures are usually analyzed numerically; there are very few closed-form solutions in the literature. In this paper, we study the pure torsion of SMA bars with circular cross sections. 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 bars in loading and unloading is obtained. Several case studies are presented in order to investigate the influence of different parameters, e.g. temperature and material properties on the torsional response of SMA circular bars.