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© 2020

Geometric Continuum Mechanics

  • Reuven Segev
  • Marcelo Epstein
Book

Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 42)

Also part of the Advances in Continuum Mechanics book sub series (ACM, volume 42)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Kinematics, Forces and Stress Theory

    1. Front Matter
      Pages 1-1
    2. Jędrzej Śniatycki, Reuven Segev
      Pages 185-219
  3. Defects, Uniformity and Homogeneity

    1. Front Matter
      Pages 221-221
    2. Marcelo Epstein, Reuven Segev
      Pages 223-265
    3. Marek Z. Elżanowski, Gareth P. Parry
      Pages 303-348
    4. Marcelo Epstein, Raz Kupferman, Cy Maor
      Pages 349-380
    5. V. M. Jiménez, M. de León, M. Epstein
      Pages 381-416
  4. Reuven Segev, Marcelo Epstein
    Pages C1-C1

About this book

Introduction

This contributed volume explores the applications of various topics in modern differential geometry to the foundations of continuum mechanics. In particular, the contributors use notions from areas such as global analysis, algebraic topology, and geometric measure theory. Chapter authors are experts in their respective areas, and provide important insights from the most recent research. Organized into two parts, the book first covers kinematics, forces, and stress theory, and then addresses defects, uniformity, and homogeneity. Specific topics covered include:
  • Global stress and hyper-stress theories
  • Applications of de Rham currents to singular dislocations
  • Manifolds of mappings for continuum mechanics
  • Kinematics of defects in solid crystals
Geometric Continuum Mechanics will appeal to graduate students and researchers in the fields of mechanics, physics, and engineering who seek a more rigorous mathematical understanding of the area. Mathematicians interested in applications of analysis and geometry will also find the topics covered here of interest.

Keywords

Continuum Mechanics Geometric Continuum Mechanics Geometry and mechanics Differential geometry Stress functions de Rham currents de Rham differential Groupoids Manifolds of Mappings Force and Stress Theory Geometry of Defects and Dislocations Analysis of Homogeneity of Material Bodies

Editors and affiliations

  • Reuven Segev
    • 1
  • Marcelo Epstein
    • 2
  1. 1.Department of Mechanical EngineeringBen-Gurion University of the NegevBeer-ShevaIsrael
  2. 2.Department of Mechanical and Manufacturing EngineeringUniversity of CalgaryCalgaryCanada

Bibliographic information