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Material Inhomogeneities and their Evolution

A Geometric Approach

  • Marcelo Epstein
  • Marek Elżanowski

Part of the Interaction Mechanics, Mathematics book series (IMM)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Inhomogeneity in Continuum Mechanics

    1. Front Matter
      Pages 1-1
    2. Marcelo Epstein, Marek Elżanowski
      Pages 3-40
    3. Marcelo Epstein, Marek Elżanowski
      Pages 41-65
    4. Marcelo Epstein, Marek Elżanowski
      Pages 67-96
    5. Marcelo Epstein, Marek Elżanowski
      Pages 97-108
  3. Material Evolution

    1. Front Matter
      Pages 109-109
    2. Marcelo Epstein, Marek Elżanowski
      Pages 111-133
    3. Marcelo Epstein, Marek Elżanowski
      Pages 135-182
    4. Marcelo Epstein, Marek Elżanowski
      Pages 183-189
  4. Mathematical Foundations

    1. Front Matter
      Pages 191-191
    2. Marcelo Epstein, Marek Elżanowski
      Pages 193-212
    3. Marcelo Epstein, Marek Elżanowski
      Pages 213-234
    4. Marcelo Epstein, Marek Elżanowski
      Pages 235-242
    5. Marcelo Epstein, Marek Elżanowski
      Pages 243-261
  5. Back Matter
    Pages 263-267

About this book

Introduction

Inhomogeneity theory is of importance for the description of a variety of material phenomena, including continuous distributions of dislocations, fracture mechanics, plasticity, biological remodelling and growth and, more generally, all processes that entail changes in the material body driven by forces known in literature as material or configurational. This monograph presents a unified treatment of the theory using some of the tools of modern differential geometry. The first part of the book deals with the geometrical description of uniform bodies and their homogeneity (i.e., integrability) conditions. In the second part, a theory of material evolution is developed and its relevance in various applied contexts discussed. The necessary geometrical notions are introduced as needed in the first two parts but often without due attention to an uncompromising mathematical rigour. This task is left for the third part of the book, which is a highly technical compendium of those concepts of modern differential geometry that are invoked in the first two parts (differentiable manifolds, Lie groups, jets, principal fibre bundles, G-structures, connections, frame bundles, integrable prolongations, groupoids, etc.). To make the text as useful as possible to active researchers and graduate students, considerable attention has been devoted to non-standard topics, such as second-grade materials, Cosserat media and functionally graded bodies.

Keywords

Cosserat media Differential Geometry Dislocations Eshelby stress Material uniformity Remodelling and growth Second-grade materials computer-aided design (CAD) continuum mechanics linear optimization mechanics modeling plasticity

Authors and affiliations

  • Marcelo Epstein
    • 1
  • Marek Elżanowski
    • 2
  1. 1.Department of Mechanical & Manufacturing EngineeringThe University of CalgaryCalgaryCanada
  2. 2.Department of Mathematics and StatisticsPortland State UniversityPortlandUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-72373-8
  • Copyright Information Springer 2007
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-540-72372-1
  • Online ISBN 978-3-540-72373-8
  • Series Print ISSN 1860-6245
  • Buy this book on publisher's site