A phenomenological model for torque-twist angle response of shape memory alloy

Abstract Helical shape memory alloy (SMA) springs can have larger actuation displacements than SMA wires. During the actuation of the SMA spring, the material undergoes torsional loading. In order to estimate the shape memory effect and the pseudoelastic response of SMA spring, the behaviour of SMA under torsional loading has to be considered. This work proposes a simple constitutive model with torque and twisting angle as the state variable. An internal variable, similar to plastic strain, captures the hysteresis behaviour. The model is developed using a non-iterative procedure for ease of implementation and computational efficiency. In the result section, suitable model parameters are identified to capture various experimental results, such as pseudoelastic response and double hysteresis effect under clockwise and anticlockwise torsional loading. After that, the response of the material under different temperatures, as well as different axial stresses, is also simulated. The temperature-dependent parameters also show that the model can capture strain recovery behaviour. Finally, using a multiyield surface model, the ability to simulate the inner loop behaviour observed in the SMA has also been demonstrated.