Configurational Forces as Basic Concepts of Continuum Physics
Springer-Verlag New York Inc.
978-1-4757-7403-0 (ISBN)
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 within a Classical Context.- Kinematics.- Standard Forces. Working.- Migrating Control Volumes. Stationary and Time-Dependent Changes in Reference Configuration.- Configurational Forces.- Thermodynamics. Relation Between Bulk Tension and Energy. Eshelby Identity.- Inertia and Kinetic Energy. Alternative Versions of the Second Law.- Change in Reference Configuration.- Elastic and Thermoelastic Materials.- The Use of Configurational Forces to Characterize Coherent Phase Interfaces.- Interface Kinematics.- Interface Forces. Second Law.- Inertia. Basic Equations for the Interface.- An Equivalent Formulation of the Theory. Infinitesimal Deformations.- Formulation within a Classical Context.- Coherent Phase Interfaces.- Evolving Interfaces Neglecting Bulk Behavior.- Evolving Surfaces.- Configurational Force System. Working.- Second Law.- Constitutive Equations. Evolution Equation for the Interface.- Two-Dimensional Theory.- Coherent Phase Interfaces wtih Interfacial Energy and Deformation.- Theory Neglecting Standard Interfacial Stress.- General Theory with Standard and Configurational Stress within the Interface.- Two-Dimensional Theory with Standard and Configurational Stress within the Interface.- Solidification.- Solidification. The Stefan Condition as a Consequence of the Configurational Force Balance.- Solidification with Interfacial Energy and Entropy.- Fracture.- Cracked Bodies.- Motions.- Forces. Working.- The Second Law.- Basic Results for the Crack Tip.- Constitutive Theory for Growing Cracks.- Kinking and Curving of Cracks. Maximum Dissipation Criterion.- Fracture in Three Space Dimensions (Results).- Two-Dimensional Theory of Corners and Junctions Neglecting Inertia.- Preliminaries. Transport Theorems.- Thermomechanical Theory of Junctionsand Corners.
| Reihe/Serie | Applied Mathematical Sciences ; 137 |
|---|---|
| Zusatzinfo | XIV, 250 p. |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Naturwissenschaften ► Physik / Astronomie ► Mechanik | |
| Technik ► Maschinenbau | |
| ISBN-10 | 1-4757-7403-6 / 1475774036 |
| ISBN-13 | 978-1-4757-7403-0 / 9781475774030 |
| Zustand | Neuware |
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