Geometric Continuum Mechanics
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Geometric Continuum Mechanics
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Author : Reuven Segev
language : en
Publisher: Springer Nature
Release Date : 2020-05-13
Geometric Continuum Mechanics written by Reuven Segev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-13 with Mathematics categories.
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.
Foundations Of Geometric Continuum Mechanics
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Author : Reuven Segev
language : en
Publisher: Springer Nature
Release Date : 2023-10-31
Foundations Of Geometric Continuum Mechanics written by Reuven Segev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-31 with Mathematics categories.
This monograph presents the geometric foundations of continuum mechanics. An emphasis is placed on increasing the generality and elegance of the theory by scrutinizing the relationship between the physical aspects and the mathematical notions used in its formulation. The theory of uniform fluxes in affine spaces is covered first, followed by the smooth theory on differentiable manifolds, and ends with the non-smooth global theory. Because continuum mechanics provides the theoretical foundations for disciplines like fluid dynamics and stress analysis, the author’s extension of the theory will enable researchers to better describe the mechanics of modern materials and biological tissues. The global approach to continuum mechanics also enables the formulation and solutions of practical optimization problems. Foundations of Geometric Continuum Mechanics will be an invaluable resource for researchers in the area, particularly mathematicians, physicists, and engineers interested in the foundational notions of continuum mechanics.
Geometric Continuum Mechanics And Induced Beam Theories
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Author : Simon R. Eugster
language : en
Publisher: Springer
Release Date : 2015-03-19
Geometric Continuum Mechanics And Induced Beam Theories written by Simon R. Eugster and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-19 with Science categories.
This research monograph discusses novel approaches to geometric continuum mechanics and introduces beams as constraint continuous bodies. In the coordinate free and metric independent geometric formulation of continuum mechanics as well as for beam theories, the principle of virtual work serves as the fundamental principle of mechanics. Based on the perception of analytical mechanics that forces of a mechanical system are defined as dual quantities to the kinematical description, the virtual work approach is a systematic way to treat arbitrary mechanical systems. Whereas this methodology is very convenient to formulate induced beam theories, it is essential in geometric continuum mechanics when the assumptions on the physical space are relaxed and the space is modeled as a smooth manifold. The book addresses researcher and graduate students in engineering and mathematics interested in recent developments of a geometric formulation of continuum mechanics and a hierarchical development of induced beam theories.
The Geometrical Language Of Continuum Mechanics
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Author : Marcelo Epstein
language : en
Publisher: Cambridge University Press
Release Date : 2010-07-26
The Geometrical Language Of Continuum Mechanics written by Marcelo Epstein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-26 with Science categories.
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.
Geometry Of Incompatible Deformations
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Author :
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-03-04
Geometry Of Incompatible Deformations written by and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-04 with Science categories.
No detailed description available for "Geometry of Incompatible Deformations".
Geometry And Continuum Mechanics
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Author : Giovanni Romano
language : en
Publisher: CreateSpace
Release Date : 2014-11-01
Geometry And Continuum Mechanics written by Giovanni Romano and has been published by CreateSpace this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-01 with categories.
Continuum Mechanics (CM) is a natural field of application of concepts and methods of Differential Geometry (DG). The very foundations of both disciplines are intertwined in a deep manner. A presentation of basic issues in CM adopting the powerful tools of modern DG is still substantially lacking. This booklet is intended to contribute to fill this gap, with specific reference to Elasticity theory. The classical subject is thoroughly revisited and revised in its basic aspects and in the general context of finite deformations. A case study of rubber-like materials enlightens the new concepts introduced by the geometric theory and opens the way for applications to soft materials such as the ones of interest in biomechanics.
Differential Geometry And Continuum Mechanics
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Author : Gui-Qiang G. Chen
language : en
Publisher: Springer
Release Date : 2015-08-11
Differential Geometry And Continuum Mechanics written by Gui-Qiang G. Chen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-11 with Mathematics categories.
This book examines the exciting interface between differential geometry and continuum mechanics, now recognised as being of increasing technological significance. Topics discussed include isometric embeddings in differential geometry and the relation with microstructure in nonlinear elasticity, the use of manifolds in the description of microstructure in continuum mechanics, experimental measurement of microstructure, defects, dislocations, surface energies, and nematic liquid crystals. Compensated compactness in partial differential equations is also treated. The volume is intended for specialists and non-specialists in pure and applied geometry, continuum mechanics, theoretical physics, materials and engineering sciences, and partial differential equations. It will also be of interest to postdoctoral scientists and advanced postgraduate research students. These proceedings include revised written versions of the majority of papers presented by leading experts at the ICMS Edinburgh Workshop on Differential Geometry and Continuum Mechanics held in June 2013. All papers have been peer reviewed.
Material Geometry Groupoids In Continuum Mechanics
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Author : Manuel De Leon
language : en
Publisher: World Scientific
Release Date : 2021-04-23
Material Geometry Groupoids In Continuum Mechanics written by Manuel De Leon and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-23 with Mathematics categories.
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.
Differential Geometry Applied To Continuum Mechanics
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Author : Daniel Aubram
language : en
Publisher:
Release Date : 2009
Differential Geometry Applied To Continuum Mechanics written by Daniel Aubram and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Material Geometry
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Author : Manuel De Leon
language : en
Publisher:
Release Date : 2021
Material Geometry written by Manuel De Leon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Algebroids categories.