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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.
Price: $196.99
Pages: 408
Publisher: De Gruyter
Imprint: De Gruyter
Publication Date:
05 November 2018
ISBN: 9783110562019
Format: Hardcover
BISACs:
MAT012000 MATHEMATICS / Geometry / General, MAT012030 MATHEMATICS / Geometry / Differential, SCI040000 SCIENCE / Physics / Mathematical & Computational, TEC021000 Technology & Engineering / Materials Science / General
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