Configurational Forces as Basic Concepts of Continuum Physics

Softcover Nachdruck of the original 1. Auflage 2000
ISBN: 978-1-4757-7403-0
Verlag: Springer

Buch, Englisch, Band 137, 250 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 417 g

Reihe: Applied Mathematical Sciences

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.

Zielgruppe

Research

Autoren/Hrsg.

Gurtin, Morton E.

Fachgebiete

• Naturwissenschaften Physik Mechanik
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Werkstoffprüfung
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Maschinenbau

Inhaltsverzeichnis

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.