Evolution of Phase Transitions: A Continuum Theory by Rohan Abeyaratne (PDF)

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a very good work by Rohan Abeyaratne and James K. Knowles who are famous persons in this field. The book has mainly been written based on the authors’ publication thought they have partially provided topics from others. The first things that comes to my mind about this book is that it is clear. It doesn’t suffer mathematical complexities and it is ideal to learn the elements of phase transformation (PT) in solids. Most of important features of PT are described in deformation of a simple 1D wire undergoing PT. Finally there is a nice connection to higher dimensional problems. They mostly have provided numerical results based on a special trilinear constitutive relation that brings a nice colsed-form explicit conclusions. They are not dealing much with convexity analysis. Most of the cases are diffusion-less PT. There is a nice description on shape-memory effect.

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