Analytical model for the torsional response of superelastic shape memory alloy circular sections subjected to a loading-unloading cycle

This paper presents a new analytical model for superelastic shape memory alloy (SMA) circular shafts subjected to pure torsion. The model considers reversible phase transformation between austenite and a single martensite variant, driven by mechanical loading. The applied torque is gradually increased from zero to a value sufficient to cause complete transformation of the austenitic phase into martensite away from the center of the shaft. The torque is then gradually removed, resulting in complete strain recovery. At each stage of the loading/unloading process, an analytical relation is established between the torque and the angle of twist. Special emphasis is placed on modeling the unloading process, for which the proposed solution significantly improves upon existing work. The analytical model is validated against high-accuracy numerical solutions and finite element analysis results.