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Home > Science, Technology & Agriculture > Mechanical engineering and materials > Materials science > Engineering: Mechanics of solids > Material Inhomogeneities and their Evolution: A Geometric Approach(Interaction of Mechanics and Mathematics)
Material Inhomogeneities and their Evolution: A Geometric Approach(Interaction of Mechanics and Mathematics)

Material Inhomogeneities and their Evolution: A Geometric Approach(Interaction of Mechanics and Mathematics)


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About the Book

Inhomogeneity theory is important for the description of a variety of material phenomena. This concise and understandable book 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. To make the text as useful as possible to active researchers and graduate students, considerable attention has been devoted to non-standard topics.



Table of Contents:
Inhomogeneity in Continuum Mechanics.- An overview of inhomogeneity theory.- Uniformity of second-grade materials.- Uniformity of Cosserat media.- Functionally graded bodies.- Material Evolution.- On energy, Cauchy stress and Eshelby stress.- An overview of the theory of material evolution.- Second-grade evolution.- Mathematical Foundations.- Basic geometric concepts.- Theory of connections.- Bundles of linear frames.- Connections of higher order.

Review :
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)


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Product Details
  • ISBN-13: 9783540723721
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Publisher Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Height: 235 mm
  • No of Pages: 261
  • Returnable: N
  • Sub Title: A Geometric Approach
  • ISBN-10: 3540723722
  • Publisher Date: 05 Sep 2007
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Series Title: Interaction of Mechanics and Mathematics
  • Width: 155 mm


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Material Inhomogeneities and their Evolution: A Geometric Approach(Interaction of Mechanics and Mathematics)
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Material Inhomogeneities and their Evolution: A Geometric Approach(Interaction of Mechanics and Mathematics)
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