A three-species model for simulating torsional response of shape memory alloy components using thermodynamic principles and discrete Preisach models

Shape memory alloy (SMA) components under torsional loading have shown the ability to deliver near-constant forces over large working strokes, thus enabling them to find various engineering applications. In this work, a model to capture the torsional response of SMA components under both superelastic and shape memory effects is formulated. A three-species Gibbs-potential-based formulation is employed to separate the thermoelastic response of the SMA from its dissipative response. The dissipative part is then modeled with a discrete Preisach approach. The proposed approach combines the elegance of the thermodynamic-based approach with the algorithmic efficiency/simplicity of the Preisach model and thus providing an effective way in predicting complex SMA responses. The model is constructed directly in terms of experimentally measurable quantities: torque and angle of twist rather than estimating them by solving for non-homogeneous shear stresses across the specimen cross-section. The model is used to predict the torsional response of SMA components such as wires, rods and springs at different twists and temperatures. Models capable of predicting torsional responses directly in terms of torque and angle of twist at different temperatures or twists under superelastic and twinning response conditions would play a pivotal role in the design of many SMA devices from both structural and control systems standpoints.