Evolution of Phase Transitions: A Continuum Theory

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Overview

This is a valuable work for 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 that in the framework of classical thermomechanics represents information that is supplementary to the usual balance principles and constitutive laws of conventional theory. The book should be of interest to mechanicians, material scientists, geophysicists, and applied mathematicians.
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Editorial Reviews

From the Publisher
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
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Product Details

  • ISBN-13: 9780521661478
  • Publisher: Cambridge University Press
  • Publication date: 2/28/2006
  • Pages: 258
  • Product dimensions: 6.97 (w) x 9.96 (h) x 0.63 (d)

Meet the Author

Rohan Abeyaratne is the Quentin Berg Professor and Department Head of Mechanical Engineering at the Massachusetts Institute of Technology. Among his many honors are: E.O.E. Pereira Gold Medal, 1975; Den Hartog Distinguished Educator, 1995; Fellow, American Academy of Mechanics; 1996 Fellow, ASME, 1998; MacVicar Faculty Fellow, 2000. His research focuses include Continuum Mechanics; Finite Elasticity and Plasticity; Material Instability and Non-Equilibrium Behavior of Solids; Stress-Induced Phase Transformations in Solids, and Cavitation.

Professor James K. Knowles is the William R. Kenan, Jr. Professor of Applied Mechanics. He received his Ph.D. from the Massachusetts Institute of Technology, D.Sc.h.c., National University of Ireland, and has received the following awards: Goodwin Medal for Effective Teaching, MIT (1955), Award of the Associated Students of Caltech for Excellence in Teaching (1984, 1985), Award of the Caltech Graduate Student Council for Exceptional Teaching (1993); Fellow, American Academy of Mechanics; Fellow, American Society of Mechanical Engineers; President of the American Academy of Mechanics, 1985-86; Eringen Medal, Society of Engineering Science (1991). He is the author of Linear Vector Spaces and Cartesian Tensors (1997) and numerous articles in refereed journals.

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Table of Contents

1 Introduction 3
2 Two-well potentials, governing equations and energetics 19
3 Equilibrium phase mixtures and quasistatic processes 32
4 Impact-induced transitions in two-phase elastic materials 59
5 Multiple-well free energy potentials 85
6 The continuum theory of driving force 105
7 Thermoelastic materials 113
8 Kinetics and nucleation 124
9 Models for two-phase thermoelastic materials in one dimension 149
10 Quasistatic hysteresis in two-phase thermoelastic tensile bars 163
11 Dynamics of phase transitions in uniaxially strained thermoelastic solids 181
12 Statics : geometric compatibility 197
13 Dynamics : impact-induced transition in a CuAINi single crystal 209
14 Quasistatics : kinetics of martensitic twinning 221
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