Abstract
Recent years have seen the successful use of continuum models--based on the minimization of an appropriate nonconvex free energy--to explain some of the complicated microstructure which is commonly observed in shape memory alloys, magnetostrictive materials, ferro- electrics, etc. However, due to their inherent static nature such models cannot provide insight into important dynamic phenomena such as: the growth of microstructure, the evolution of phase boundaries, or the eventual fate of metastable structures. We describe the behavior of some simple dynamical models of shape-memory alloys which display the formation of microstructure. The focus is on models whose underlying bulk free energy do not attain a minimum, possessing sequences of configurations with finer and finer microstructure that converge weakly to nonminimizing states. The effects of viscoelastic damping on the stability of steady state solutions, the propagation of phase boundaries, and the long-time approach to minimum energy states is discussed.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
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