Configurational Forces as Basic Concepts of Continuum Physics

Morton E. Gurtin (auth.)0387986677, 9780387986678, 9780387226569

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.

---

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