Material Inhomogeneities and their Evolution

A Geometric Approach

Marcelo Epstein, Marek Elzanowski (Autoren)

Buch | Softcover

XIII, 261 Seiten

2007 | 2007
Springer Berlin (Verlag)
978-3-540-72372-1 (ISBN)

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With its origins in the theories of continuous distributions of dislocations and ofmetalplasticity,inhomogeneitytheoryisarichandvibrant?eldofresearch. The recognition of the important role played by con?gurational or material forces in phenomena such as growth and remodelling is perhaps its greatest present-day impetus. While some excellent comprehensive works approa- ing the subject from di?erent angles have been published, the objective of this monograph is to present a point of view that emphasizes the di?erenti- geometric aspects of inhomogeneity theory. In so doing, we follow the general lines of thought that we have propounded in many publications and presen- tions over the last two decades. Although based on these sources, this book is a stand-alone entity and contains some new results and perspectives. At the same time, it does not intend to present either a historical account of the - velopment of the subject or a comprehensive picture of the various schools of thought that can be encountered by perusing scholarly journals and attending specialized symposia. The book is divided into three parts, the ?rst of which is entirely devoted to the formulation of the theory in the absence of evolution. In other words, time is conspicuously absent from Part I. It opens with the geometric ch- acterization of material inhomogeneity within the context of simple bodies in Chapter 1, followed by extensions to second-grade and Cosserat media in Chapters 2 and 3.

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.

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.

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)

Erscheint lt. Verlag	5.9.2007
Reihe/Serie	Interaction of Mechanics and Mathematics
Zusatzinfo	XIII, 261 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	439 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Themenwelt	Technik ► Maschinenbau
Schlagworte	Computer-Aided Design (CAD) • Continuum Mechanics • Cosserat media • Differential Geometry • dislocations • Eshelby stress • linear optimization • Material uniformity • Mechanics • Modeling • Plasticity • Remodelling and growth • Second-grade materials
ISBN-10	3-540-72372-2 / 3540723722
ISBN-13	978-3-540-72372-1 / 9783540723721
Zustand	Neuware