Marcelo Epstein, Marek Elzanowski

Material Inhomogeneities and their Evolution (eBook, PDF)

A Geometric Approach

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 261
• Erscheinungstermin: 3. August 2007
• Englisch
• ISBN-13: 9783540723738
• Artikelnr.: 37365802

Autorenporträt

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.

Inhaltsangabe

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.

Rezensionen

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)