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