Interaction of Mechanics and Mathematics

Material Inhomogeneities and their Evolution

A Geometric Approach

Authors: Epstein, Marcelo, Elzanowski, Marek

  • Concise and understandable book about material inhomogeneities and their evolution
  • Accessible to applied mathematicians, physicists and engineers who have an interest in materials inhomgeneities
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eBook $129.00
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  • ISBN 978-3-540-72373-8
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Softcover $169.00
price for USA
  • ISBN 978-3-540-72372-1
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About this book

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.

Reviews

From the reviews:

"The objective of the present book is to present a point of view that emphasizes the differential-geometric aspect of the inhomogeneity theory. By following the presentation in the preface, the book is divided in three parts … . This book is highly recommended to the workers on modern continuum mechanics." (Franco Cardin, Zentralblatt MATH, Vol. 1130 (8), 2008)

"The main goal of this book is to present a new point of view on the theory of material inhomogeneities by means of a strong mathematical tool, namely, differential geometry. … useful for a reader who is interested in one of the particular topics treated. … I recommend it as one of the best monographs not only on the topic of material inhomogeneities, but even in the larger domain of the differential-geometric approach to continuum mechanics." (Nicolae Boja, Mathematical Reviews, Issue 2009 e)


Table of contents (11 chapters)

  • An overview of inhomogeneity theory

    Epstein, Marcelo (et al.)

    Pages 3-40

  • Uniformity of second-grade materials

    Epstein, Marcelo (et al.)

    Pages 41-65

  • Uniformity of Cosserat media

    Epstein, Marcelo (et al.)

    Pages 67-96

  • Functionally graded bodies

    Epstein, Marcelo (et al.)

    Pages 97-108

  • On energy, Cauchy stress and Eshelby stress

    Epstein, Marcelo (et al.)

    Pages 111-133

Buy this book

eBook $129.00
price for USA (gross)
  • ISBN 978-3-540-72373-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $169.00
price for USA
  • ISBN 978-3-540-72372-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Material Inhomogeneities and their Evolution
Book Subtitle
A Geometric Approach
Authors
Series Title
Interaction of Mechanics and Mathematics
Copyright
2007
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-72373-8
DOI
10.1007/978-3-540-72373-8
Softcover ISBN
978-3-540-72372-1
Series ISSN
1860-6245
Edition Number
1
Number of Pages
XIII, 261
Topics