Differential Geometry And Continuum Mechanics PDF Download
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Author | : Reuven Segev |
Publisher | : Springer Nature |
Total Pages | : 416 |
Release | : 2020-05-13 |
Genre | : Mathematics |
ISBN | : 3030426831 |
Download Geometric Continuum Mechanics Book 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.
Author | : Gui-Qiang G. Chen |
Publisher | : Springer |
Total Pages | : 384 |
Release | : 2015-08-11 |
Genre | : Mathematics |
ISBN | : 331918573X |
Download Differential Geometry and Continuum Mechanics Book in PDF, ePub and Kindle
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.
Author | : |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 370 |
Release | : 2019-03-04 |
Genre | : Science |
ISBN | : 3110563215 |
Download Geometry of Incompatible Deformations Book in PDF, ePub and Kindle
Author | : Marcelo Epstein |
Publisher | : Springer |
Total Pages | : 147 |
Release | : 2014-07-02 |
Genre | : Mathematics |
ISBN | : 3319069209 |
Download Differential Geometry Book in PDF, ePub and Kindle
Differential Geometry offers a concise introduction to some basic notions of modern differential geometry and their applications to solid mechanics and physics. Concepts such as manifolds, groups, fibre bundles and groupoids are first introduced within a purely topological framework. They are shown to be relevant to the description of space-time, configuration spaces of mechanical systems, symmetries in general, microstructure and local and distant symmetries of the constitutive response of continuous media. Once these ideas have been grasped at the topological level, the differential structure needed for the description of physical fields is introduced in terms of differentiable manifolds and principal frame bundles. These mathematical concepts are then illustrated with examples from continuum kinematics, Lagrangian and Hamiltonian mechanics, Cauchy fluxes and dislocation theory. This book will be useful for researchers and graduate students in science and engineering.
Author | : Marcelo Epstein |
Publisher | : Cambridge University Press |
Total Pages | : 325 |
Release | : 2010-07-26 |
Genre | : Science |
ISBN | : 113949046X |
Download The Geometrical Language of Continuum Mechanics Book 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.
Author | : Daniel Aubram |
Publisher | : |
Total Pages | : 99 |
Release | : 2009 |
Genre | : |
ISBN | : 9783832281540 |
Download Differential Geometry Applied to Continuum Mechanics Book in PDF, ePub and Kindle
Author | : Paul Steinmann |
Publisher | : Springer |
Total Pages | : 534 |
Release | : 2015-03-25 |
Genre | : Science |
ISBN | : 3662464608 |
Download Geometrical Foundations of Continuum Mechanics Book in PDF, ePub and Kindle
This book illustrates the deep roots of the geometrically nonlinear kinematics of generalized continuum mechanics in differential geometry. Besides applications to first- order elasticity and elasto-plasticity an appreciation thereof is particularly illuminating for generalized models of continuum mechanics such as second-order (gradient-type) elasticity and elasto-plasticity. After a motivation that arises from considering geometrically linear first- and second- order crystal plasticity in Part I several concepts from differential geometry, relevant for what follows, such as connection, parallel transport, torsion, curvature, and metric for holonomic and anholonomic coordinate transformations are reiterated in Part II. Then, in Part III, the kinematics of geometrically nonlinear continuum mechanics are considered. There various concepts of differential geometry, in particular aspects related to compatibility, are generically applied to the kinematics of first- and second- order geometrically nonlinear continuum mechanics. Together with the discussion on the integrability conditions for the distortions and double-distortions, the concepts of dislocation, disclination and point-defect density tensors are introduced. For concreteness, after touching on nonlinear fir st- and second-order elasticity, a detailed discussion of the kinematics of (multiplicative) first- and second-order elasto-plasticity is given. The discussion naturally culminates in a comprehensive set of different types of dislocation, disclination and point-defect density tensors. It is argued, that these can potentially be used to model densities of geometrically necessary defects and the accompanying hardening in crystalline materials. Eventually Part IV summarizes the above findings on integrability whereby distinction is made between the straightforward conditions for the distortion and the double-distortion being integrable and the more involved conditions for the strain (metric) and the double-strain (connection) being integrable. The book addresses readers with an interest in continuum modelling of solids from engineering and the sciences alike, whereby a sound knowledge of tensor calculus and continuum mechanics is required as a prerequisite.
Author | : John D Clayton |
Publisher | : World Scientific |
Total Pages | : 193 |
Release | : 2014-07-31 |
Genre | : Mathematics |
ISBN | : 9814616052 |
Download Differential Geometry And Kinematics Of Continua Book in PDF, ePub and Kindle
This book provides definitions and mathematical derivations of fundamental relationships of tensor analysis encountered in nonlinear continuum mechanics and continuum physics, with a focus on finite deformation kinematics and classical differential geometry. Of particular interest are anholonomic aspects arising from a multiplicative decomposition of the deformation gradient into two terms, neither of which in isolation necessarily obeys the integrability conditions satisfied by the gradient of a smooth vector field. The concise format emphasizes clarity and ease of reference, and detailed step-by-step derivations of most analytical results are provided.
Author | : Manuel De Leon |
Publisher | : World Scientific |
Total Pages | : 226 |
Release | : 2021-04-23 |
Genre | : Mathematics |
ISBN | : 9811232563 |
Download Material Geometry: Groupoids In Continuum Mechanics Book 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.
Author | : F. William Lawvere |
Publisher | : Springer |
Total Pages | : 131 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540397604 |
Download Categories in Continuum Physics Book in PDF, ePub and Kindle