Applied Mathematical Sciences

By: Morton E. Gurtin

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Hardcover | 29 December 1999

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272 Pages

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23.39 x 15.6 x 1.6

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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.

Industry Reviews

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."

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You Can Find This Book In

Non-Fiction Mathematics Applied Mathematics Science Physics Classical Mathematics Wave Mechanics including Vibration & Acoustics

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Paperback

Published: 16th March 2013

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Introduction	p. 1
Configurational forces within a classical context	p. 19
Kinematics	p. 21
Standard forces. Working	p. 25
Migrating control volumes. Stationary and time-dependent changes in reference configuration	p. 29
Configurational forces	p. 34
Thermodynamics. Relation between bulk tension and energy. Eshelby identity	p. 41
Inertia and kinetic energy. Alternative versions of the second law	p. 46
Change in reference configuration	p. 50
Elastic and thermoelastic materials	p. 53
The use of configurational forces to characterize coherent phase interfaces	p. 61
Interface kinematics	p. 63
Interface forces. Second law	p. 66
Inertia. Basic equations for the interface	p. 74
An equivalent formulation of the theory. Infinitesimal deformations	p. 81
Formulation within a classical context	p. 83
Coherent phase interfaces	p. 88
Evolving interfaces neglecting bulk behavior	p. 91
Evolving surfaces	p. 93
Configurational force system. Working	p. 101
Second law	p. 108
Constitutive equations	p. 110
Two-dimensional theory	p. 115
Coherent phase interfaces with interfacial energy and deformation	p. 127
Theory neglecting standard interfacial stress	p. 129
General theory with standard and configurational stress within the interface	p. 138
Two-dimensional theory with standard and configurational stress within the interface	p. 149
Solidification	p. 157
Solidification. The Stefan condition as a consequence of the configurational force balance	p. 159
Solidification with interfacial energy and entropy	p. 163
Fracture	p. 173
Cracked bodies	p. 175
Motions	p. 182
Forces. Working	p. 184
The second law	p. 190
Basic results for the crack tip	p. 196
Constitutive theory for growing cracks	p. 198
Kinking and curving of cracks. Maximum dissipation criterion	p. 201
Fracture in three space dimensions (results)	p. 208
Two-dimensional theory of corners and junctions neglecting inertia	p. 211
Preliminaries. Transport theorems	p. 213
Thermomechanical theory of junctions and corners	p. 218
Appendices on the principle of virtual work for coherent phase interfaces	p. 225
Weak principle of virtual work	p. 227
Strong principle of virtual work	p. 232
References	p. 239
Index	p. 247
Table of Contents provided by Blackwell. All Rights Reserved.

Applied Mathematical Sciences

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

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