Elements of Continuum Mechanics and Conservation Laws

1. Auflage. Softcover version of original hardcover Auflage 2003
ISBN: 978-1-4419-3399-7
Verlag: Springer US

Buch, Englisch, 258 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 417 g

Elements of Continuum Mechanics and Conservation Laws presents a systematization of different models in mathematical physics, a study of the structure of conservation laws, thermodynamical identities, and connection with criteria for well-posedness of the corresponding mathematical problems.
The theory presented in this book stems from research carried out by the authors concerning the formulations of differential equations describing explosive deformations of metals. In such processes, elasticity equations are used in some zones, whereas hydrodynamics equations are stated in other zones. Plastic deformations appear in transition zones, which leads to residual stresses. The suggested model contains some relaxation terms which simulate these plastic deformations. Certain laws of thermodynamics are used in order to describe and study differential equations simulating the physical processes. This leads to the special formulation of differential equations using generalized thermodynamical potentials.

Zielgruppe

Research

Autoren/Hrsg.

Romenskii, Evgenii I.

Godunov, S.K.

Fachgebiete

• Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
• Naturwissenschaften Physik Mechanik Kontinuumsmechanik, Strömungslehre
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik
• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
• Mathematik | Informatik EDV | Informatik Informatik
• Naturwissenschaften Physik Mechanik Klassische Mechanik, Newtonsche Mechanik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Strömungslehre
• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Werkstoffprüfung

Inhaltsverzeichnis

I. Elementary Properties of Deformations and Stresses.- II. Effective Elastic Deformation.- III. Differential Equations of Dynamical Processes.- IV. Well-Posedness of Differential Equations and Thermodynamics.- V. Multi-Dimensional Thermodynamically Compatible Conservation Laws.- Appendix. Structure of Thermodynamically Compatible Systems — S. K. Godunov.- § 1. Mathematical Aspects.- § 2. The Simplest Galilei-Invariant Thermodynamically Compatible Systems.- § 3. Methods of Constructing Equations.- § 4. Some Facts of the Theory of Representations of Orthogonal Transformations of Three-Dimensional Space.- § 5. The Clebsch—Gordan Coefficients.- § 6. Orthogonal Invariants.- Literature.