Introduction To Geometrically Nonlinear Continuum Dislocation Theory
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Introduction To Geometrically Nonlinear Continuum Dislocation Theory
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Author : Christian B. Silbermann
language : en
Publisher: Springer Nature
Release Date : 2021-03-02
Introduction To Geometrically Nonlinear Continuum Dislocation Theory written by Christian B. Silbermann and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-02 with Technology & Engineering categories.
This book provides an introduction to geometrically non-linear single crystal plasticity with continuously distributed dislocations. A symbolic tensor notation is used to focus on the physics. The book also shows the implementation of the theory into the finite element method. Moreover, a simple simulation example demonstrates the capability of the theory to describe the emergence of planar lattice defects (subgrain boundaries) and introduces characteristics of pattern forming systems. Numerical challenges involved in the localization phenomena are discussed in detail.
Geometrical Foundations Of Continuum Mechanics
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Author : Paul Steinmann
language : en
Publisher: Springer
Release Date : 2015-03-25
Geometrical Foundations Of Continuum Mechanics written by Paul Steinmann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-25 with Science categories.
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.
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.
Generalized Continua From The Theory To Engineering Applications
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Author : Holm Altenbach
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-17
Generalized Continua From The Theory To Engineering Applications written by Holm Altenbach and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-17 with Science categories.
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.
Analysis And Computation Of Microstructure In Finite Plasticity
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Author : Sergio Conti
language : en
Publisher: Springer
Release Date : 2015-04-23
Analysis And Computation Of Microstructure In Finite Plasticity written by Sergio Conti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-23 with Science categories.
This book addresses the need for a fundamental understanding of the physical origin, the mathematical behavior and the numerical treatment of models which include microstructure. Leading scientists present their efforts involving mathematical analysis, numerical analysis, computational mechanics, material modelling and experiment. The mathematical analyses are based on methods from the calculus of variations, while in the numerical implementation global optimization algorithms play a central role. The modeling covers all length scales, from the atomic structure up to macroscopic samples. The development of the models ware guided by experiments on single and polycrystals and results will be checked against experimental data.
Journal Of The Mechanical Behavior Of Materials
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Author :
language : en
Publisher:
Release Date : 2000
Journal Of The Mechanical Behavior Of Materials written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Deformations (Mechanics) categories.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2008
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
A Nonlinear Progress To Modern Soliton Theory
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Author : Colin Rogers
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2022-12-06
A Nonlinear Progress To Modern Soliton Theory written by Colin Rogers and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-06 with Mathematics categories.
This book provides a historical account of the discovery in 1834 of a remarkable singular wave that was ultimately to lead to the development of modern soliton theory with its diverse physical applications. In terms of associated geometry, the classical work of Bäcklund and Bianchi and its consequences is recounted, notably with regard to nonlinear superposition principles, which later were shown to be generic to soliton systems and which provide the analytic description of complex multi-soliton interaction. Whereas the applications of modern soliton in certain areas of physics are well-documented, deep connections between soliton theory and nonlinear continuum mechanics have had a separate development. This book describes wide applications in such disparate areas as elastostatics, elastodynamics, superelasticity, shell theory, magnetohydrostatics and magnetohydrodynamics, and will appeal to research scientists and advanced students with an interest in integrable systems in nonlinear physics or continuum mechanics.
Mesoscale Models
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Author : Sinisa Mesarovic
language : en
Publisher: Springer
Release Date : 2018-11-19
Mesoscale Models written by Sinisa Mesarovic and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-19 with Science categories.
The book helps to answer the following questions: How far have the understanding and mesoscale modeling advanced in recent decades, what are the key open questions that require further research and what are the mathematical and physical requirements for a mesoscale model intended to provide either insight or a predictive engineering tool? It is addressed to young researchers including doctoral students, postdocs and early career faculty,
Nonlinear Elastic And Inelastic Models For Shock Compression Of Crystalline Solids
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Author : John D. Clayton
language : en
Publisher: Springer
Release Date : 2019-05-17
Nonlinear Elastic And Inelastic Models For Shock Compression Of Crystalline Solids written by John D. Clayton and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-17 with Science categories.
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.