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Material Inhomogeneities and their Evolution A Geometric Approach by Marcelo Epstein, Marek Elzanowski

Material Inhomogeneities and their Evolution A Geometric Approach


Part of the Interaction of Mechanics and Mathematics Series


Material Inhomogeneities and their Evolution A Geometric Approach by Marcelo Epstein, Marek Elzanowski

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.


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)

About the Author

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Book Info

Publication date

5th September 2007


Marcelo Epstein, Marek Elzanowski

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Springer-Verlag Berlin and Heidelberg GmbH & Co. K an imprint of Springer-Verlag Berlin and Heidelberg GmbH & Co. KG


261 pages


Mechanical engineering & materials
Maths for engineers
Applied mathematics
Classical mechanics



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