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Differential Geometry and Continuum Mechanics

  • Conference proceedings
  • © 2015

Overview

Editors:
  1. Gui-Qiang G. Chen

    1. Radcliffe Observatory Quarter, Mathematical Institute, Oxford, United Kingdom

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  2. Michael Grinfeld

    1. Department of Mathematics and Statistics Livingstone Tower, University of Strathclyde, Glasgow, United Kingdom

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    You can also search for this editor in PubMed   Google Scholar

  3. R. J. Knops

    1. School of Mathem. and Computer Science, Heriot-Watt University, Edinburgh, United Kingdom

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 137)

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Table of contents (13 papers)

  1. Front Matter

    Pages i-viii
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  2. General

    1. Front Matter

      Pages 1-1
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    2. Compensated Compactness with More Geometry

      • Luc Tartar
      Pages 3-26

  4. Defects and Microstructure

    1. Front Matter

      Pages 121-121
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    2. Continuum Mechanics of the Interaction of Phase Boundaries and Dislocations in Solids

      • Amit Acharya, Claude Fressengeas
      Pages 123-165

    3. Manifolds in a Theory of Microstructures

      • G. Capriz, R. J. Knops
      Pages 167-201

    4. On the Geometry and Kinematics of Smoothly Distributed and Singular Defects

      • Marcelo Epstein, Reuven Segev
      Pages 203-234

    5. Non-metricity and the Nonlinear Mechanics of Distributed Point Defects

      • Arash Yavari, Alain Goriely
      Pages 235-251

  5. Solids

    1. Front Matter

      Pages 253-253
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    2. Are Microcontinuum Field Theories of Elasticity Amenable to Experiments? A Review of Some Recent Results

      • Christian Liebold, Wolfgang H. Müller
      Pages 255-278

    3. On the Variational Limits of Lattice Energies on Prestrained Elastic Bodies

      • Marta Lewicka, Pablo Ochoa
      Pages 279-305

    4. Static Elasticity in a Riemannian Manifold

      • Cristinel Mardare
      Pages 307-342

  6. Fluids and Liquid Crystals

    1. Front Matter

      Pages 343-343
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    2. Calculating the Bending Moduli of the Canham–Helfrich Free-Energy Density

      • Brian Seguin, Eliot Fried
      Pages 345-361

    3. Elasticity of Twist-Bend Nematic Phases

      • Epifanio G. Virga
      Pages 363-380

  7. Back Matter

    Pages 381-387
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Keywords

About this book

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.

Editors and Affiliations

  • Radcliffe Observatory Quarter, Mathematical Institute, Oxford, United Kingdom

    Gui-Qiang G. Chen

  • Department of Mathematics and Statistics Livingstone Tower, University of Strathclyde, Glasgow, United Kingdom

    Michael Grinfeld

  • School of Mathem. and Computer Science, Heriot-Watt University, Edinburgh, United Kingdom

    R. J. Knops

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