Differential Geometry And Kinematics Of Continua

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Differential Geometry and Kinematics of Continua

John D Clayton
Differential Geometry and Kinematics of Continua Book PDF

Author : John D Clayton
Publisher : World Scientific
Page : 192 pages
File Size : 41,6 Mb
Release : 2014-07-31
Category : Mathematics
ISBN : 9789814616058

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Differential Geometry and Kinematics of Continua by John D Clayton Pdf

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. Contents: IntroductionGeometric FundamentalsKinematics of Integrable DeformationGeometry of Anholonomic DeformationKinematics of Anholonomic DeformationList of SymbolsBibliographyIndex Readership: Researchers in mathematical physics and engineering mechanics. Key Features:Presentation of mathematical operations and examples in anholonomic space associated with a multiplicative decomposition (e.g., of the gradient of motion) is more general and comprehensive than any given elsewhere and contains original ideas and new resultsLine-by-line derivations are frequent and exhaustive, to facilitate practice and enable verification of final resultsGeneral analysis is given in generic curvilinear coordinates; particular sections deal with applications and examples in Cartesian, cylindrical, spherical, and convected coordinates. Indicial and direct notations of tensor calculus enable connections with historic and modern literature, respectivelyKeywords:Differential Geometry;Tensor Analysis;Continuum Mechanics;Kinematics;Deformation;Anholonomic Coordinates

Geometric Continuum Mechanics

Reuven Segev,Marcelo Epstein
Geometric Continuum Mechanics Book PDF

Author : Reuven Segev,Marcelo Epstein
Publisher : Springer Nature
Page : 416 pages
File Size : 41,8 Mb
Release : 2020-05-13
Category : Mathematics
ISBN : 9783030426835

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Geometric Continuum Mechanics by Reuven Segev,Marcelo Epstein Pdf

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.

Differential Geometry

Marcelo Epstein
Differential Geometry Book PDF

Author : Marcelo Epstein
Publisher : Springer
Page : 139 pages
File Size : 50,6 Mb
Release : 2014-07-02
Category : Mathematics
ISBN : 9783319069203

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Differential Geometry by Marcelo Epstein Pdf

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.

Geometrical Foundations of Continuum Mechanics

Paul Steinmann
Geometrical Foundations of Continuum Mechanics Book PDF

Author : Paul Steinmann
Publisher : Springer
Page : 517 pages
File Size : 52,5 Mb
Release : 2015-03-25
Category : Science
ISBN : 9783662464601

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Geometrical Foundations of Continuum Mechanics by Paul Steinmann Pdf

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.

Nonlinear Elastic and Inelastic Models for Shock Compression of Crystalline Solids

John D. Clayton
Nonlinear Elastic and Inelastic Models for Shock Compression of Crystalline Solids Book PDF

Author : John D. Clayton
Publisher : Springer
Page : 483 pages
File Size : 48,8 Mb
Release : 2019-05-17
Category : Science
ISBN : 9783030153304

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Nonlinear Elastic and Inelastic Models for Shock Compression of Crystalline Solids by John D. Clayton Pdf

This book describes thermoelastic and inelastic deformation processes in crystalline solids undergoing loading by shock compression. Constitutive models with a basis in geometrically nonlinear continuum mechanics supply these descriptions. Large deformations such as finite strains and rotations, are addressed. The book covers dominant mechanisms of nonlinear thermoelasticity, dislocation plasticity, deformation twinning, fracture, flow, and other structure changes. Rigorous derivations of theoretical results are provided, with approximately 1300 numbered equations and an extensive bibliography of over 500 historical and modern references spanning from the 1920s to the present day. Case studies contain property data, as well as analytical, and numerical solutions to shock compression problems for different materials. Such materials are metals, ceramics, and minerals, single crystalline and polycrystalline. The intended audience of this book is practicing scientists (physicists, engineers, materials scientists, and applied mathematicians) involved in advanced research on shock compression of solid materials.

Generalized Continua - from the Theory to Engineering Applications

Holm Altenbach,Victor A. Eremeyev
Generalized Continua from the Theory to Engineering Applications Book PDF

Author : Holm Altenbach,Victor A. Eremeyev
Publisher : Springer Science & Business Media
Page : 403 pages
File Size : 41,8 Mb
Release : 2012-10-18
Category : Technology & Engineering
ISBN : 9783709113707

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Generalized Continua - from the Theory to Engineering Applications by Holm Altenbach,Victor A. Eremeyev Pdf

On the roots of continuum mechanics in differential geometry -- a review.- Cosserat media.- Cosserat-type shells.- Cosserat-type rods.- Micromorphic media.- Electromagnetism and generalized continua.- Computational methods for generalized continua. The need of generalized continua models is coming from practice. Complex material behavior sometimes cannot be presented by the classical Cauchy continua. At present the attention of the scientists in this field is focused on the most recent research items • new models, • application of well-known models to new problems, • micro-macro aspects, • computational effort, and • possibilities to identify the constitutive equations The new research directions are discussed in this volume - from the point of view of modeling and simulation, identification, and numerical methods.

Differential Geometry: Geometry in Mathematical Physics and Related Topics

Robert Everist Greene,Shing-Tung Yau
Differential Geometry Geometry in Mathematical Physics and Related Topics Book PDF

Author : Robert Everist Greene,Shing-Tung Yau
Publisher : American Mathematical Soc.
Page : 681 pages
File Size : 55,7 Mb
Release : 1993
Category : Complex manifolds
ISBN : 9780821814956

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Differential Geometry: Geometry in Mathematical Physics and Related Topics by Robert Everist Greene,Shing-Tung Yau Pdf

The second of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Among the subjects of Part 2 are gauge theory, symplectic geometry, complex ge

Kinematic Differential Geometry and Saddle Synthesis of Linkages

Delun Wang,Wei Wang
Kinematic Differential Geometry and Saddle Synthesis of Linkages Book PDF

Author : Delun Wang,Wei Wang
Publisher : John Wiley & Sons
Page : 450 pages
File Size : 43,7 Mb
Release : 2015-05-11
Category : Technology & Engineering
ISBN : 9781118255063

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Kinematic Differential Geometry and Saddle Synthesis of Linkages by Delun Wang,Wei Wang Pdf

With a pioneering methodology, the book covers the fundamental aspects of kinematic analysis and synthesis of linkage, and provides a theoretical foundation for engineers and researchers in mechanisms design. • The first book to propose a complete curvature theory for planar, spherical and spatial motion • Treatment of the synthesis of linkages with a novel approach • Well-structured format with chapters introducing clearly distinguishable concepts following in a logical sequence dealing with planar, spherical and spatial motion • Presents a pioneering methodology by a recognized expert in the field and brought up to date with the latest research and findings • Fundamental theory and application examples are supplied fully illustrated throughout

Introductory Differential Geometry For Physicists

A Visconti
Introductory Differential Geometry For Physicists Book PDF

Author : A Visconti
Publisher : World Scientific Publishing Company
Page : 424 pages
File Size : 47,7 Mb
Release : 1992-10-09
Category : Electronic
ISBN : 9789813103887

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Introductory Differential Geometry For Physicists by A Visconti Pdf

This book develops the mathematics of differential geometry in a way more intelligible to physicists and other scientists interested in this field. This book is basically divided into 3 levels; level 0, the nearest to intuition and geometrical experience, is a short summary of the theory of curves and surfaces; level 1 repeats, comments and develops upon the traditional methods of tensor algebra analysis and level 2 is an introduction to the language of modern differential geometry. A final chapter (chapter IV) is devoted to fibre bundles and their applications to physics. Exercises are provided to amplify the text material.

Differential Geometry with Applications to Mechanics and Physics

Yves Talpaert
Differential Geometry with Applications to Mechanics and Physics Book PDF

Author : Yves Talpaert
Publisher : CRC Press
Page : 480 pages
File Size : 46,6 Mb
Release : 2000-09-12
Category : Mathematics
ISBN : 0824703855

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Differential Geometry with Applications to Mechanics and Physics by Yves Talpaert Pdf

An introduction to differential geometry with applications to mechanics and physics. It covers topology and differential calculus in banach spaces; differentiable manifold and mapping submanifolds; tangent vector space; tangent bundle, vector field on manifold, Lie algebra structure, and one-parameter group of diffeomorphisms; exterior differential forms; Lie derivative and Lie algebra; n-form integration on n-manifold; Riemann geometry; and more. It includes 133 solved exercises.

Geometric Design of Linkages

J. Michael McCarthy
Geometric Design of Linkages Book PDF

Author : J. Michael McCarthy
Publisher : Springer Science & Business Media
Page : 320 pages
File Size : 47,6 Mb
Release : 2006-04-06
Category : Mathematics
ISBN : 9780387227351

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Geometric Design of Linkages by J. Michael McCarthy Pdf

An introduction to the mathematical theory of design for articulated mechanical systems known as linkages. This book will be useful to mathematics, engineering and computer science departments that teach courses on mathematical modelling of robotics and other articulated mechanical systems.

Looking Beyond The Frontiers Of Science: Dedicated To The 80th Birthday Of Kk Phua

Lars Brink,Ngee-pong Chang,Kazuo Fujikawa,Da-hsuan Feng,Mo-lin Ge,Leong-chuan Kwek,Spenta R Wadia
Looking Beyond The Frontiers Of Science Dedicated To The 80th Birthday Of Kk Phua Book PDF

Author : Lars Brink,Ngee-pong Chang,Kazuo Fujikawa,Da-hsuan Feng,Mo-lin Ge,Leong-chuan Kwek,Spenta R Wadia
Publisher : World Scientific
Page : 341 pages
File Size : 43,6 Mb
Release : 2022-07-25
Category : Science
ISBN : 9789811263705

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Looking Beyond The Frontiers Of Science: Dedicated To The 80th Birthday Of Kk Phua by Lars Brink,Ngee-pong Chang,Kazuo Fujikawa,Da-hsuan Feng,Mo-lin Ge,Leong-chuan Kwek,Spenta R Wadia Pdf

Professor Kok Khoo Phua is the Founding Director and Emeritus Professor of the Institute of Advanced Studies (IAS) at Nanyang Technological University (NTU) and Adjunct Professor of Department of Physics both at Nanyang Technological University (NTU) and National University of Singapore (NUS). He is the Chairman and Editor-in-Chief of World Scientific Publishing Co Pte Ltd.When he was elected a Fellow of the American Physical Society (APS) in 2009, the citation read: 'For tireless efforts to strengthen scientific research throughout Asia and promote international physics education and scholarly exchanges, and for enriching science and education through the World Scientific Publishing Company he founded.'This unique volume on the occasion of his 80th birthday is a compilation of tributes from his friends who have known him for decades along with scientific articles that celebrate his visionary approach to promote science worldwide.

Computational Contact Mechanics

Alexander Konyukhov,Karl Schweizerhof
Computational Contact Mechanics Book PDF

Author : Alexander Konyukhov,Karl Schweizerhof
Publisher : Springer Science & Business Media
Page : 446 pages
File Size : 41,6 Mb
Release : 2012-08-14
Category : Science
ISBN : 9783642315312

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Computational Contact Mechanics by Alexander Konyukhov,Karl Schweizerhof Pdf

This book contains a systematical analysis of geometrical situations leading to contact pairs -- point-to-surface, surface-to-surface, point-to-curve, curve-to-curve and curve-to-surface. Each contact pair is inherited with a special coordinate system based on its geometrical properties such as a Gaussian surface coordinate system or a Serret-Frenet curve coordinate system. The formulation in a covariant form allows in a straightforward fashion to consider various constitutive relations for a certain pair such as anisotropy for both frictional and structural parts. Then standard methods well known in computational contact mechanics such as penalty, Lagrange multiplier methods, combination of both and others are formulated in these coordinate systems. Such formulations require then the powerful apparatus of differential geometry of surfaces and curves as well as of convex analysis. The final goals of such transformations are then ready-for-implementation numerical algorithms within the finite element method including any arbitrary discretization techniques such as high order and isogeometric finite elements, which are most convenient for the considered geometrical situation. The book proposes a consistent study of geometry and kinematics, variational formulations, constitutive relations for surfaces and discretization techniques for all considered geometrical pairs and contains the associated numerical analysis as well as some new analytical results in contact mechanics.

Tensor Calculus and Differential Geometry for Engineers

Shahab Sahraee,Peter Wriggers
Tensor Calculus and Differential Geometry for Engineers Book PDF

Author : Shahab Sahraee,Peter Wriggers
Publisher : Springer Nature
Page : 684 pages
File Size : 42,9 Mb
Release : 2023-12-12
Category : Technology & Engineering
ISBN : 9783031339530

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Tensor Calculus and Differential Geometry for Engineers by Shahab Sahraee,Peter Wriggers Pdf

The book contains the basics of tensor algebra as well as a comprehensive description of tensor calculus, both in Cartesian and curvilinear coordinates. Some recent developments in representation theorems and differential forms are included. The last part of the book presents a detailed introduction to differential geometry of surfaces and curves which is based on tensor calculus. By solving numerous exercises, the reader is equipped to properly understand the theoretical background and derivations. Many solved problems are provided at the end of each chapter for in-depth learning. All derivations in this text are carried out line by line which will help the reader to understand the basic ideas. Each figure in the book includes descriptive text that corresponds with the theoretical derivations to facilitate rapid learning.

Applied Nanoindentation in Advanced Materials

Atul Tiwari,Sridhar Natarajan
Applied Nanoindentation in Advanced Materials Book PDF

Author : Atul Tiwari,Sridhar Natarajan
Publisher : John Wiley & Sons
Page : 704 pages
File Size : 43,7 Mb
Release : 2017-10-30
Category : Technology & Engineering
ISBN : 9781119084495

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Applied Nanoindentation in Advanced Materials by Atul Tiwari,Sridhar Natarajan Pdf

Research in the area of nanoindentation has gained significant momentum in recent years, but there are very few books currently available which can educate researchers on the application aspects of this technique in various areas of materials science. Applied Nanoindentation in Advanced Materials addresses this need and is a comprehensive, self-contained reference covering applied aspects of nanoindentation in advanced materials. With contributions from leading researchers in the field, this book is divided into three parts. Part one covers innovations and analysis, and parts two and three examine the application and evaluation of soft and ceramic-like materials respectively. Key features: A one stop solution for scholars and researchers to learn applied aspects of nanoindentation Contains contributions from leading researchers in the field Includes the analysis of key properties that can be studied using the nanoindentation technique Covers recent innovations Includes worked examples Applied Nanoindentation in Advanced Materials is an ideal reference for researchers and practitioners working in the areas of nanotechnology and nanomechanics, and is also a useful source of information for graduate students in mechanical and materials engineering, and chemistry. This book also contains a wealth of information for scientists and engineers interested in mathematical modelling and simulations related to nanoindentation testing and analysis.