A Nonlinear Thermodynamic Model for Phase Transitions in Shape Memory Alloy Wires

Speaker: Dr. Daniel R. Reynolds, Postdoctoral Research Staff Member, Center for Applied Scientific Computing, Lawrence Livermore National Laboratory

Smart materials are characterized by their unique ability to undergo dramatic changes in their physical structure upon application of relatively small thermal or electromagnetic loading. For this reason, smart materials such as shape memory alloys and ferromagnets have become promising candidates for various applications, including vibration damping and nanomachinery. In this talk I introduce a continuum-thermodynamic model for describing these solid-state phase transformations in shape memory alloy wires. The resulting model is given by the solution of a nonlinear, ill-posed hyperbolic-parabolic system of equations. This system of equations is discretized using space-time Galerkin methods, allowing for uniform treatment of space and time while maintaining discrete conservation laws. The resulting finite-dimensional, nonlinear, non-convex system is solved using a continuation method that combines regularization and Newton's method in order to surpass the moments of phase transition. I conclude the talk by presenting results of computational experiments demonstrating first the ability of the model to reproduce thermally- and stress-induced phase transitions in shape memory alloy wires, and second an application toward thermally-controlled vibration damping.

Last modified: Wed Oct 8 13:09:24 EDT 2003