Material Geometry: Groupoids In Continuum Mechanics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Material Geometry: Groupoids In Continuum Mechanics write by Manuel De Leon. This book was released on 2021-04-23. Material Geometry: Groupoids In Continuum Mechanics available in PDF, EPUB and Kindle. This monograph is the first in which the theory of groupoids and algebroids is applied to the study of the properties of uniformity and homogeneity of continuous media. It is a further step in the application of differential geometry to the mechanics of continua, initiated years ago with the introduction of the theory of G-structures, in which the group G denotes the group of material symmetries, to study smoothly uniform materials.The new approach presented in this book goes much further by being much more general. It is not a generalization per se, but rather a natural way of considering the algebraic-geometric structure induced by the so-called material isomorphisms. This approach has allowed us to encompass non-uniform materials and discover new properties of uniformity and homogeneity that certain material bodies can possess, thus opening a new area in the discipline.
Geometric Continuum Mechanics
Geometric Continuum Mechanics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Continuum Mechanics write by Reuven Segev. This book was released on 2020-05-13. Geometric Continuum Mechanics available in PDF, EPUB and Kindle. This contributed volume explores the applications of various topics in modern differential geometry to the foundations of continuum mechanics. In particular, the contributors use notions from areas such as global analysis, algebraic topology, and geometric measure theory. Chapter authors are experts in their respective areas, and provide important insights from the most recent research. Organized into two parts, the book first covers kinematics, forces, and stress theory, and then addresses defects, uniformity, and homogeneity. Specific topics covered include: Global stress and hyper-stress theories Applications of de Rham currents to singular dislocations Manifolds of mappings for continuum mechanics Kinematics of defects in solid crystals Geometric Continuum Mechanics will appeal to graduate students and researchers in the fields of mechanics, physics, and engineering who seek a more rigorous mathematical understanding of the area. Mathematicians interested in applications of analysis and geometry will also find the topics covered here of interest.
The Geometrical Language of Continuum Mechanics
The Geometrical Language of Continuum Mechanics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Geometrical Language of Continuum Mechanics write by Marcelo Epstein. This book was released on 2010-07-26. The Geometrical Language of Continuum Mechanics available in PDF, EPUB and Kindle. Epstein presents the fundamental concepts of modern differential geometry within the framework of continuum mechanics. Divided into three parts of roughly equal length, the book opens with a motivational chapter to impress upon the reader that differential geometry is indeed the natural language of continuum mechanics or, better still, that the latter is a prime example of the application and materialisation of the former. In the second part, the fundamental notions of differential geometry are presented with rigor using a writing style that is as informal as possible. Differentiable manifolds, tangent bundles, exterior derivatives, Lie derivatives, and Lie groups are illustrated in terms of their mechanical interpretations. The third part includes the theory of fiber bundles, G-structures, and groupoids, which are applicable to bodies with internal structure and to the description of material inhomogeneity. The abstract notions of differential geometry are thus illuminated by practical and intuitively meaningful engineering applications.
Material Inhomogeneities and their Evolution
Material Inhomogeneities and their Evolution - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Material Inhomogeneities and their Evolution write by Marcelo Epstein. This book was released on 2007-09-05. Material Inhomogeneities and their Evolution available in PDF, EPUB and Kindle. 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.
Topology and Groupoids
Topology and Groupoids - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Topology and Groupoids write by Ronald Brown. This book was released on 2006. Topology and Groupoids available in PDF, EPUB and Kindle. Annotation. The book is intended as a text for a two-semester course in topology and algebraic topology at the advanced undergraduate orbeginning graduate level. There are over 500 exercises, 114 figures, numerous diagrams. The general direction of the book is towardhomotopy theory with a geometric point of view. This book would providea more than adequate background for a standard algebraic topology coursethat begins with homology theory. For more information seewww.bangor.ac.uk/r.brown/topgpds.htmlThis version dated April 19, 2006, has a number of corrections made.
