Evolution of phase transitions : a continuum theory
 Responsibility
 Rohan Abeyaratne, James K. Knowles.
 Language
 English.
 Imprint
 Cambridge ; New York : Cambridge University Press, 2006.
 Physical description
 xv, 242 p. : ill. ; 27 cm.
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QC175.16 .P5 A24 2006  Available 
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Creators/Contributors
 Author/Creator
 Abeyaratne, Rohan.
 Contributor
 Knowles, James K. (James Kenyon), 1931
Contents/Summary
 Bibliography
 Includes bibliographical references and indexes.
 Contents

 Part I. Introduction: 1. What this monograph is about 2. Some experiments 3. Continuum mechanics 4. Quasilinear systems 5. Outline of monograph Part II. TwoWell Potentials, Governing Equations and Energetics: 1. Introduction 2. Twophase nonlinearly elastic materials 3. Field equations and jump conditions 4. Energetics of motion, driving force and dissipation inequality Part III. Equilibrium Phase Mixtures and Quasistatic Processes: 1. Introduction 2. Equilibrium states 3. Variational theory of equilibrium mixtures of phases 4. Quasistatic processes 5. Nucleation and kinetics 6. Constant elongation rate processes 7. Hysteresis Part IV. ImpactInduced Transitions in TwoPhase Elastic Materials: 1. Introduction 2. The impact problem for trilinear twophase materials 3. Scaleinvariant solutions of the impact problem 4. Nucleation and kinetics 5. Comparison with experiment 6. Other types of kinetic relations 7. Related work Part V. MultipleWell Free Energy Potentials: 1. Introduction 2. Helmholtz free energy potential 3. Potential energy function and the effect of stress 4. Example 1: The van der Waals fluid 5. Example 2: Twophase martensitic material with cubic and tetragonal phases Part VI. The Continuum Theory of Driving Force: 1. Introduction 2. Balance laws, field equations and jump conditions 3. The second law of thermodynamics and the driving force Part VII. Thermoelastic Materials: 1. Introduction 2. The thermoelastic constitutive law 3. Stability of a thermoelastic material 4. A onedimensional special case: uniaxial strain Part VIII. Kinetics and Nucleation: 1. Introduction 2. Nonequilibrium processes, thermodynamic fluxes and forces, kinetic relation 3. Phenomenological examples of kinetic relations 4. Micromechanicallybased examples of kinetic relations 5. Nucleation Part IX. Models for TwoPhase Thermoelastic Materials in One Dimension: 1. Preliminaries 2. Materials of MieGruneisen type 3. Twophase MieGruneisen materials Part X. Quasistatic Hysteresis in TwoPhase Thermoelastic Tensile Bars: 1. Preliminaries 2. Thermomechanical equilibrium states for a twophase material 3. Quasistatic processes 4. Trilinear thermoelastic material 5. Stress cycles at constant temperature 6. Temperature cycles at constant stress 7. The shapememory cycle 8. The experiments of Shaw and Kyriakides 9. Slow thermomechanical processes Part XI. Dynamics of Phase Transitions in Uniaxially Strained Thermoelastic Solids: 1. Introduction 2. Uniaxial strain in adiabatic thermoelasticity 3. The impact problem Part XII. Statics: Geometric Compatibility: 1. Preliminaries 2. Examples Part XIII. Dynamics: ImpactInduced Transition in a CuA1Nl Single Crystal: 1. Introduction 2. Preliminaries 3. Impact without phase transformation 4. Impact with phase transformation 5. Application to austeniteB1 martensite transformation in CuA1Nl Part XIV. Quasistatics: Kinetics of Martensitic Twinning: 1. Introduction 2. The material and loading device 3. Observations 4. The model 5. The energy of the system 6. The effect of the transition layers: further observations 7. The effect of the transition layers: further modeling 8. Kinetics.
 (source: Nielsen Book Data)9780521661478 20160528
 Publisher's Summary
 This 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 is an essential work to those interested in the development and application of continuummechanical models that describe the macroscopic response of materials capable of undergoing stress or temperatureinduced transitions between two solid phases. The focus is on the evolution of phase transitions which may be either dynamic or quasistatic, 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. The book should be of interest to mechanicians, materials scientists, geophysicists, and applied mathematicians.
(source: Nielsen Book Data)9780521661478 20160528  Supplemental links

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Bibliographic information
 Publication date
 2006
 ISBN
 0521661471
 9780521661478