Finite element modeling of cyclic thermal response of shape memory alloy wires with variable material properties

This paper considers the influence of variable thermal conductivity and electrical resistivity on the cyclic thermal response of a shape memory alloy (SMA) wire. The specific boundary value problem of an SMA wire under zero-stress conditions is considered, wherein the wire, in an initially martensitic state, is heated by electrical current and cooled by convection. An isothermal boundary condition is considered at the ends of the wire. The heating is continued until the transformation from martensite to austenite has essentially taken place. A Galerkin finite element method (FEM)-based numerical approach is used to solve the boundary value problem. The two key parameters of interest are the maximum possible transformation achievable (i.e. extent of actuation) and the time period for one cycle. It is seen that for short wires, the assumption of constant thermal conductivity underestimates the actuation and overestimates the cycle time significantly. The assumption of a constant electrical resistivity does not affect the actuation but significantly overestimates the cycle time. For long wires, the thermal conductivity effect is diminished whereas the electrical resistivity effect is very similar to that for the short wires.