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.
Rezensionen / Stimmen
"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
Reihe
Sprache
Verlagsort
Zielgruppe
Für Beruf und Forschung
US School Grade: College Graduate Student
Illustrationen
37 s/w Abbildungen, 14 s/w Tabellen
37 b/w ill., 14 b/w tbl.
Maße
Höhe: 246 mm
Breite: 175 mm
Dicke: 28 mm
Gewicht
ISBN-13
978-3-11-056201-9 (9783110562019)
Schweitzer Klassifikation
Sergey Lychev
and
Konstantin Koifman
, Institute for Problems in Mechanics of Russian Academy of Science, Russia.
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
