Material Inhomogeneities and their Evolution (eBook)

A Geometric Approach

Marcelo Epstein, Marek Elzanowski (Autoren)

eBook Download: PDF

2007 | 2007
XIII, 261 Seiten
Springer Berlin (Verlag)
978-3-540-72373-8 (ISBN)

Infos

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.

Inhalt

Preface 6
Contents 8
Part I Inhomogeneity in Continuum Mechanics 13
1 An overview of inhomogeneity theory 14
2 Uniformity of second-grade materials 52
3 Uniformity of Cosserat media 77
4 Functionally graded bodies 107
Part II Material Evolution 119
5 On energy, Cauchy stress and Eshelby stress 120
6 An overview of the theory of material evolution 143
7 Second-grade evolution 191
Part III Mathematical Foundations 198
8 Basic geometric concepts 199
9 Theory of connections 219
10 Bundles of linear frames 241
11 Connections of higher order 249
A Groupoids 263
References 268
Index 273

Produkt-Details

• Erscheint lt. Verlag: 3.8.2007
• Reihe/Serie: Interaction of Mechanics and Mathematics
• Reihe/Serie: Interaction of Mechanics and Mathematics
• Zusatzinfo: XIII, 261 p.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• 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: 3-540-72373-0 / 3540723730
• ISBN-13: 978-3-540-72373-8 / 9783540723738