A subspace thermodynamic model for shape memory alloy wire elements undergoing combined thermo-mechanical axial and torsional loads

Given that most applications of shape memory alloys (SMA) are in the wire form, a reduced order model and analysis has been attempted in this paper. It takes into account the fact that the predominant actions are axial (bending inclusive) and torsional. A thermodynamic framework is first developed to simulate the behaviour of the SMA material under thermo-mechanical loading that is a combination of axial and shear stresses arising at a point in a wire due to axial and torsional loads applied to the wire. Since only a few variants relevant to axial-torsion are going to be active in transformation under this kind of loading, a reduced order model that tracks the evolution of four martensite variants and an austenite variant is proposed. It is shown through simulations that these five model parameters amply form a minimal set of model parameters sufficient for simulating response under tension-torsion loading excursions. The model is further applied to the structural member, in this case, a wire of circular cross-section subject to a twist and an axial extension and the capability of the model to simulate the kind of response expected in wires. Incorporation of this model into a large deformation space frame nonlinear analysis will help in the design and analysis of several applications where SMA wire forms are used.