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Configurational Forces as Basic Concepts of Continuum Physics : Applied Mathematical Sciences - Morton E. Gurtin

Configurational Forces as Basic Concepts of Continuum Physics

Applied Mathematical Sciences

Hardcover

Published: 29th December 1999
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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.

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."

Introductionp. 1
Configurational forces within a classical contextp. 19
Kinematicsp. 21
Standard forces. Workingp. 25
Migrating control volumes. Stationary and time-dependent changes in reference configurationp. 29
Configurational forcesp. 34
Thermodynamics. Relation between bulk tension and energy. Eshelby identityp. 41
Inertia and kinetic energy. Alternative versions of the second lawp. 46
Change in reference configurationp. 50
Elastic and thermoelastic materialsp. 53
The use of configurational forces to characterize coherent phase interfacesp. 61
Interface kinematicsp. 63
Interface forces. Second lawp. 66
Inertia. Basic equations for the interfacep. 74
An equivalent formulation of the theory. Infinitesimal deformationsp. 81
Formulation within a classical contextp. 83
Coherent phase interfacesp. 88
Evolving interfaces neglecting bulk behaviorp. 91
Evolving surfacesp. 93
Configurational force system. Workingp. 101
Second lawp. 108
Constitutive equationsp. 110
Two-dimensional theoryp. 115
Coherent phase interfaces with interfacial energy and deformationp. 127
Theory neglecting standard interfacial stressp. 129
General theory with standard and configurational stress within the interfacep. 138
Two-dimensional theory with standard and configurational stress within the interfacep. 149
Solidificationp. 157
Solidification. The Stefan condition as a consequence of the configurational force balancep. 159
Solidification with interfacial energy and entropyp. 163
Fracturep. 173
Cracked bodiesp. 175
Motionsp. 182
Forces. Workingp. 184
The second lawp. 190
Basic results for the crack tipp. 196
Constitutive theory for growing cracksp. 198
Kinking and curving of cracks. Maximum dissipation criterionp. 201
Fracture in three space dimensions (results)p. 208
Two-dimensional theory of corners and junctions neglecting inertiap. 211
Preliminaries. Transport theoremsp. 213
Thermomechanical theory of junctions and cornersp. 218
Appendices on the principle of virtual work for coherent phase interfacesp. 225
Weak principle of virtual workp. 227
Strong principle of virtual workp. 232
Referencesp. 239
Indexp. 247
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387986678
ISBN-10: 0387986677
Series: Applied Mathematical Sciences
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 250
Published: 29th December 1999
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.4 x 15.6  x 2.54
Weight (kg): 1.24