Geometry of Incompatible Deformations

Differential Geometry in Continuum Mechanics
1. Auflage 2024
ISBN: 978-3-11-056201-9
Verlag: De Gruyter

Buch, Englisch, 388 Seiten, Format (B × H): 175 mm x 246 mm, Gewicht: 871 g

Reihe: ISSN

This monograph provides a systematic treatment of differential geometry in modeling of incompatible fiite deformations in solids. Included are discussions of generalized deformations and stress measures on smooth manifolds, geometrical formalizations for structurally inhomogeneous bodies, representations for configurational forces, and evolution equations.

Zielgruppe

Researchers in Mechanics, Physics, Mathematics, Mechanical Engine

Autoren/Hrsg.

Lychev, Sergey

Koifman, Konstantin

Fachgebiete

• Naturwissenschaften Physik Mechanik Kontinuumsmechanik, Strömungslehre
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Kontinuumsmechanik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

Frontmatter -- Preface -- Contents -- General Scheme of Notations -- 1. Introduction -- 2. Geometry of Physical Space -- 3. Essentials of Non-Linear Elasticity Theory -- 4. Geometric Formalization of the Body and Its Representation in Physical Space -- 5. Strain Measures -- 6. Motion -- 7. Stress Measures -- 8. Material Uniformity and Inhomogeneity -- 9. Material Connections -- 10. Balance Equations -- 11. The Evolutionary Problem – Examples -- 12. Algebraic Structures -- 13. Review of Smooth Manifolds and Vector Bundles -- 14. Connections on Principal Bundles -- Bibliography -- Index

Über Autor(innen)

Sergey Lychev and Konstantin Koifman, Institute for Problems in Mechanics of Russian Academy of Science, Russia.