Sergey Lychev, Konstantin Koifman

Geometry of Incompatible Deformations

Differential Geometry in Continuum Mechanics

• Gebundenes Buch

Produktbeschreibung

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.

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Produktdetails

• De Gruyter Studies in Mathematical Physics 50
• Verlag: De Gruyter
• Seitenzahl: 410
• Erscheinungstermin: 6. Februar 2024
• Englisch
• Abmessung: 246mm x 175mm x 28mm
• Gewicht: 824g
• ISBN-13: 9783110562019
• ISBN-10: 3110562014
• Artikelnr.: 49495824

Autorenporträt

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

Inhaltsangabe

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

Rezensionen

"This monograph is highly recommended for scholars and advanced graduate students working in areas of continuum mechanics and continuum physics, especially those with a focus on geometric methods. Applied mathematicians conducting research in nonlinear elasticity should nd the work particularly interesting and useful."
John D. Clayton in: Mathematical Reviews Clippings (2019), MR3931699