Overview

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.

Full Product Details

Author:   Sergey Lychev ,  Konstantin Koifman
Publisher:   De Gruyter
Imprint:   De Gruyter
Volume:   50
Dimensions:   Width: 17.00cm , Height: 2.50cm , Length: 24.00cm
Weight:   0.817kg
ISBN:  

9783110562019

ISBN 10:   3110562014
Pages:   408
Publication Date:   05 November 2018
Audience:   Professional and scholarly ,  Professional & Vocational ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In stock  
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Table of Contents

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

Reviews

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

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

Author Information

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

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