Configurational Forces as Basic Concepts of Continuum Physics

1. Front Matter

   Pages i-xiii

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2. Introduction

   1. Introduction

      Pages 1-17

3. Configurational Forces within a Classical Context

   1. Front Matter

      Pages 19-19

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   2. Kinematics

      Pages 21-24

   3. Standard Forces. Working

      Pages 25-28

   4. Migrating Control Volumes. Stationary and Time-Dependent Changes in Reference Configuration

      Pages 29-33

   5. Configurational Forces

      Pages 34-40

   6. Thermodynamics. Relation Between Bulk Tension and Energy. Eshelby Identity

      Pages 41-45

   7. Inertia and Kinetic Energy. Alternative Versions of the Second Law

      Pages 46-49

   8. Change in Reference Configuration

      Pages 50-52

   9. Elastic and Thermoelastic Materials

      Pages 53-59

4. The Use of Configurational Forces to Characterize Coherent Phase Interfaces

   1. Front Matter

      Pages 61-61

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   2. Interface Kinematics

      Pages 63-65

   3. Interface Forces. Second Law

      Pages 66-73

   4. Inertia. Basic Equations for the Interface

      Pages 74-80

5. An Equivalent Formulation of the Theory. Infinitesimal Deformations

   1. Front Matter

      Pages 81-81

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   2. Formulation within a Classical Context

      Pages 83-87

   3. Coherent Phase Interfaces

      Pages 88-90

6. Evolving Interfaces Neglecting Bulk Behavior

   1. Front Matter

      Pages 91-91

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   2. Evolving Surfaces

      Pages 93-100

For the last decade, the author has been working to extend continuum mechanics to treat moving boundaries in materials focusing, in particular, on problems of metallurgy. This monograph presents a rational treatment of the notion of configurational forces; it is an effort to promote a new viewpoint. Included is a presentation of configurational forces within a classical context and a discussion of their use in areas as diverse as phase transitions and fracture. The work should be of interest to materials scientists, mechanicians, and mathematicians.

• Configurational Forces
• Metall
• continuum mechanics
• continuum physics
• deformation
• fracture
• kinematics
• mechanics
• stress
• thermodynamics

From the reviews:

SIAM REVIEW

"This important book presents the development, within the framework of continuum mechanics, of the mathematical theory of such accretive forces…The monograph is a clearly and concisely written collection of short chapters…The framework provided by the use of configurational as well as standard forces is convincingly set out in an elegant and unifying manner and is applicable to a variety of significant issues in continuum mechanics. The author has produced a book that is certain to be of great importance to many workers in the mechanics and physics of continua."

MATHEMATICAL REVIEWS

"…the more original contributions in the book devoted to interfaces and solidifications are extremely interesting. They obviously correspond to the specific domain to which the author has powerfully contributed with great ingenuity and talent."

• Department of Mathematics, Carnegie Mellon University, Pittsburgh, USA

  Morton E. Gurtin

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