Exact solutions for isothermal cyclic torsional loading of a circular SMA bar exploiting the shape memory effect

• Analytical models are presented for a SMA circular bar subjected to direct and reversed torsional loading. The distributions of shear stress Martensite variants calculated analytically at each stage. A closed form torque-twist relation is the entire process. approach validated against similar results available in literature. Application seismic response dissipative systems based on helical springs envisaged. Two simple fully analytical or wire cross section fully-reversed cyclic loading, by taking into consideration reorientation martensitic occurring during unloading reverse process assumed take place constant temperature between start temperatures austenitic transformations. In first part this work, same modulus taken both Austenite. second part, different elastic moduli considered two phases. volume fractions positive negative twisted evolve linearly with stress. initially state As applied torque increased transformation starts from outer surface then it extends inwards. If maximum large enough, complete Martensitic takes region section. During subsequent loading may occur starting boundary intermediate transforming region. Particular attention focused modeling processes. At stage, radial variant analytically. angle twist case equal moduli, only stages moduli. analytical, numerical experimental literature loading–unloading also