Material Inhomogeneities and their Evolution

1. Front Matter

   Pages I-XIII

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2. Inhomogeneity in Continuum Mechanics

   1. Front Matter

      Pages 1-1

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   2. An overview of inhomogeneity theory

      • Marcelo Epstein, Marek Elżanowski

      Pages 3-40

   3. Uniformity of second-grade materials

      • Marcelo Epstein, Marek Elżanowski

      Pages 41-65

   4. Uniformity of Cosserat media

      • Marcelo Epstein, Marek Elżanowski

      Pages 67-96

   5. Functionally graded bodies

      • Marcelo Epstein, Marek Elżanowski

      Pages 97-108

3. Material Evolution

   1. Front Matter

      Pages 109-109

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   2. On energy, Cauchy stress and Eshelby stress

      • Marcelo Epstein, Marek Elżanowski

      Pages 111-133

   3. An overview of the theory of material evolution

      • Marcelo Epstein, Marek Elżanowski

      Pages 135-182

   4. Second-grade evolution

      • Marcelo Epstein, Marek Elżanowski

      Pages 183-189

4. Mathematical Foundations

   1. Front Matter

      Pages 191-191

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   2. Basic geometric concepts

      • Marcelo Epstein, Marek Elżanowski

      Pages 193-212

   3. Theory of connections

      • Marcelo Epstein, Marek Elżanowski

      Pages 213-234

   4. Bundles of linear frames

      • Marcelo Epstein, Marek Elżanowski

      Pages 235-242

   5. Connections of higher order

      • Marcelo Epstein, Marek Elżanowski

      Pages 243-261

5. Back Matter

   Pages 263-267

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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.

• Cosserat media
• Differential Geometry
• Dislocations
• Eshelby stress
• Material uniformity
• Remodelling and growth
• Second-grade materials
• computer-aided design (CAD)
• continuum mechanics
• linear optimization
• mechanics
• modeling
• plasticity

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)

• Department of Mechanical & Manufacturing Engineering, The University of Calgary, Calgary, Canada

  Marcelo Epstein

• Department of Mathematics and Statistics, Portland State University, Portland, USA

  Marek Elżanowski

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