Configurational Forces as Basic Concepts of Continuum Physics

Morton E. Gurtin (auth.)9780387986678, 0-387-98667-7

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.

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Table of contents :
Front Matter….Pages i-xiii
Introduction….Pages 1-17
Front Matter….Pages 19-19
Kinematics….Pages 21-24
Standard Forces. Working….Pages 25-28
Migrating Control Volumes. Stationary and Time-Dependent Changes in Reference Configuration….Pages 29-33
Configurational Forces….Pages 34-40
Thermodynamics. Relation Between Bulk Tension and Energy. Eshelby Identity….Pages 41-45
Inertia and Kinetic Energy. Alternative Versions of the Second Law….Pages 46-49
Change in Reference Configuration….Pages 50-52
Elastic and Thermoelastic Materials….Pages 53-59
Front Matter….Pages 61-61
Interface Kinematics….Pages 63-65
Interface Forces. Second Law….Pages 66-73
Inertia. Basic Equations for the Interface….Pages 74-80
Front Matter….Pages 81-81
Formulation within a Classical Context….Pages 83-87
Coherent Phase Interfaces….Pages 88-90
Front Matter….Pages 91-91
Evolving Surfaces….Pages 93-100
Configurational Force System. Working….Pages 101-107
Second Law….Pages 108-109
Constitutive Equations. Evolution Equation for the Interface….Pages 110-114
Two-Dimensional Theory….Pages 115-125
Front Matter….Pages 127-127
Theory Neglecting Standard Interfacial Stress….Pages 129-137
Front Matter….Pages 127-127
General Theory with Standard and Configurational Stress within the Interface….Pages 138-148
Two-Dimensional Theory with Standard and Configurational Stress within the Interface….Pages 149-156
Front Matter….Pages 157-157
Solidification. The Stefan Condition as a Consequence of the Configurational Force Balance….Pages 159-162
Solidification with Interfacial Energy and Entropy….Pages 163-171
Front Matter….Pages 173-173
Cracked Bodies….Pages 175-181
Motions….Pages 182-183
Forces. Working….Pages 184-189
The Second Law….Pages 190-195
Basic Results for the Crack Tip….Pages 196-197
Constitutive Theory for Growing Cracks….Pages 198-200
Kinking and Curving of Cracks. Maximum Dissipation Criterion….Pages 201-207
Fracture in Three Space Dimensions (Results)….Pages 208-209
Front Matter….Pages 211-211
Preliminaries. Transport Theorems….Pages 213-217
Thermomechanical Theory of Junctions and Corners….Pages 218-224
Back Matter….Pages 225-249