A nonlinear thermodynamic model for phase transitions in shape memory alloy wires

Through a mathematical and computational model of the physical behavior of shape memory alloy wires, this study shows that localized heating and cooling of such materials provides an effective means of damping vibrational energy. The thermally induced pseudo-elastic behavior of a shape memory wire is modeled using a continuum thermodynamic description based on an improved Landau-Devonshire potential. Our construction of the potential function allows the model to account for particular alloys as well as the general solid-state phase transformation, improving over traditional potentials that idealize many of the material properties or focus only on individual processes. The material’s thermodynamic response is modeled using a nonlinear conservation of momentum and a nonlinear heat equation. The heat equation introduces an inhomogeneous version of the Fourier heat flux, thereby describing the discontinuous heat flow associated with shape memory materials more thoroughly than standard, continuous heat dissipation mechanisms do. This continuum thermodynamic model is then solved computationally to determine the resulting state of the wire in time. Continuous time Galerkin methods and affine finite element