Evolution of Phase Transitions: A Continuum Theory

Description

This 2006 work began with the author's exploration of the applicability of the finite deformation theory of elasticity when various standard assumptions such as convexity of various energies or ellipticity of the field equations of equilibrium are relinquished. The finite deformation theory of elasticity turns out to be a natural vehicle for the study of phase transitions in solids where thermal effects can be neglected. This text will be of interest to those interested in the development and application of continuum-mechanical models that describe the macroscopic response of materials capable of undergoing stress- or temperature-induced transitions between two solid phases. The focus is on the evolution of phase transitions which may be either dynamic or quasi-static, controlled by a kinetic relation which in the framework of classical thermomechanics represents information that is supplementary to the usual balance principles and constitutive laws of conventional theory.

Review of the hardback: 'Wherever possible, Abeyaratne and Knowles connect phenomenological and experimental results. Aside from comparisons between analytical predictions and experiments on shape-memory wires, the authors use their framework to model experiments involving phase transformations induced by high-speed impact. To some extent, links between atomistic and continuum models for kinetics are also explored. This book is a unique, valuable, and elegantly written contribution to the literature on phase transformations. It should be included in the library of any mechanician, applied mathematician, or material scientist interested in martensitic alloys. Others working on broader classes of phase transformations will also find this book to be worthwhile reading. It is physically well-motivated, mathematically sound, and eminently clear.' Theoretical and Computational Fluid Dynamics