Overview

This book examines the exciting interface between differential geometry and continuum mechanics, now recognised as being of increasing technological significance. Topics discussed include isometric embeddings in differential geometry and the relation with microstructure in nonlinear elasticity, the use of manifolds in the description of microstructure in continuum mechanics, experimental measurement of microstructure, defects, dislocations, surface energies, and nematic liquid crystals. Compensated compactness in partial differential equations is also treated. The volume is intended for specialists and non-specialists in pure and applied geometry, continuum mechanics, theoretical physics, materials and engineering sciences, and partial differential equations. It will also be of interest to postdoctoral scientists and advanced postgraduate research students. These proceedings include revised written versions of the majority of papers presented by leading experts at the ICMS Edinburgh Workshop on Differential Geometry and Continuum Mechanics held in June 2013. All papers have been peer reviewed.

Full Product Details

Author:   Gui-Qiang G. Chen ,  Michael Grinfeld ,  R. J. Knops
Publisher:   Springer International Publishing AG
Imprint:   Springer International Publishing AG
Edition:   Softcover reprint of the original 1st ed. 2015
Volume:   137
Weight:   6.692kg
ISBN:  

9783319371337

ISBN 10:   3319371339
Pages:   387
Publication Date:   22 October 2016
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

Compensated compactness with more geometry.- GLOBAL ISOMETRIC EMBEDDING OF SURFACES IN R3.- Singular perturbation problems involving curvature.- Lectures on the Isometric Embedding Problem(Mn, g) → IRm, m = n2 (n + 1).- Continuum mechanics of the interaction of phase boundaries and dislocations in solids.- Manifolds in a theory of microstructures.- On the Geometry and Kinematics of Smoothly Distributed and Singular Defects.- Non-Metricity and the Nonlinear Mechanics of Distributed Point Defects.- Are microcontinuum field theories of elasticity amenable to experiments? – A review of some recent results.- ON THE VARIATIONAL LIMITS OF LATTICE ENERGIES ON PRESTRAINED ELASTIC BODIES.- Static Elasticity in a Riemannian Manifold.- Calculating the bending moduli of the Canham-Helfrich free-energy density.- Elasticity of Twist-Bend Nematic Phases.

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