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Evolution of Phase Transitions
A Continuum Theory

$57.00 (C)

  • Date Published: July 2011
  • availability: Available
  • format: Paperback
  • isbn: 9780521380515
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About the Authors
  • 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.

    • This work concerns 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
    • Models the thermal and mechanical loading of alloys
    • Models the effect of high-speed projectile impact experiments on metallic or ceramic targets
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    Reviews & endorsements

    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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    04th Jun 2014 by Cr7

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    Product details

    • Date Published: July 2011
    • format: Paperback
    • isbn: 9780521380515
    • length: 260 pages
    • dimensions: 254 x 178 x 14 mm
    • weight: 0.46kg
    • availability: Available
  • Table of 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. Two-Well Potentials, Governing Equations and Energetics:
    1. Introduction
    2. Two-phase 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. Impact-Induced Transitions in Two-Phase Elastic Materials:
    1. Introduction
    2. The impact problem for trilinear two-phase materials
    3. Scale-invariant solutions of the impact problem
    4. Nucleation and kinetics
    5. Comparison with experiment
    6. Other types of kinetic relations
    7. Related work
    Part V. Multiple-Well 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: two-phase 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 one-dimensional 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. Micromechanically-based examples of kinetic relations
    5. Nucleation
    Part IX. Models for Two-Phase Thermoelastic Materials in One Dimension:
    1. Preliminaries
    2. Materials of Mie-Gruneisen type
    3. Two-phase Mie-Gruneisen materials
    Part X. Quasistatic Hysteresis in Two-Phase Thermoelastic Tensile Bars:
    1. Preliminaries
    2. Thermomechanical equilibrium states for a two-phase material
    3. Quasistatic processes
    4. Trilinear thermoelastic material
    5. Stress cycles at constant temperature
    6. Temperature cycles at constant stress
    7. The shape-memory 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: Impact-Induced Transition in a CuA1Nl Single Crystal:
    1. Introduction
    2. Preliminaries
    3. Impact without phase transformation
    4. Impact with phase transformation
    5. Application to austenite-B1 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.

  • Authors

    Rohan Abeyaratne, Massachusetts Institute of Technology

    James K. Knowles, California Institute of Technology

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