Nonlocal Continuum Field Theories
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Nonlocal Continuum Field Theories
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Author : A. Cemal Eringen
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-14
Nonlocal Continuum Field Theories written by A. Cemal Eringen 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 2007-06-14 with Science categories.
Nonlocal continuum field theories are concerned with material bodies whose behavior at any interior point depends on the state of all other points in the body -- rather than only on an effective field resulting from these points -- in addition to its own state and the state of some calculable external field. Nonlocal field theory extends classical field theory by describing the responses of points within the medium by functionals rather than functions (the "constitutive relations" of classical field theory). Such considerations are already well known in solid-state physics, where the nonlocal interactions between the atoms are prevalent in determining the properties of the material. The tools developed for crystalline materials, however, do not lend themselves to analyzing amorphous materials, or materials in which imperfections are a major part of the structure. Nonlocal continuum theories, by contrast, can describe these materials faithfully at scales down to the lattice parameter. This book presents a unified approach to field theories for elastic solids, viscous fluids, and heat-conducting electromagnetic solids and fluids that include nonlocal effects in both space and time (memory effects). The solutions to the field equations agree remarkably well with atomic theories and experimental observations.
Nonlocal Continuum Limits Of P Laplacian Problems On Graphs
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Author : Imad El Bouchairi
language : en
Publisher: Cambridge University Press
Release Date : 2023-05-11
Nonlocal Continuum Limits Of P Laplacian Problems On Graphs written by Imad El Bouchairi 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 2023-05-11 with Computers categories.
In this Element, the authors consider fully discretized p-Laplacian problems (evolution, boundary value and variational problems) on graphs. The motivation of nonlocal continuum limits comes from the quest of understanding collective dynamics in large ensembles of interacting particles, which is a fundamental problem in nonlinear science, with applications ranging from biology to physics, chemistry and computer science. Using the theory of graphons, the authors give a unified treatment of all the above problems and establish the continuum limit for each of them together with non-asymptotic convergence rates. They also describe an algorithmic framework based proximal splitting to solve these discrete problems on graphs.
Continuum Physics Polar And Non Local Field Theories
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Author : A. Cemal Eringen
language : en
Publisher:
Release Date : 1971
Continuum Physics Polar And Non Local Field Theories written by A. Cemal Eringen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Science categories.
The Non Linear Field Theories Of Mechanics
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Author : C. Truesdell
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
The Non Linear Field Theories Of Mechanics written by C. Truesdell 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 2013-03-09 with Science categories.
Non-Linear Field Theories of Mechanics has become a classic treatise in the field of continuum mechanics. Originally published nearly forty years ago, it probably has influenced practically all subsequent monographs on the subject. Its main parts are: - The General Theory of Material Behavior - Elasticity - Fluidity This third edition includes the corrections made by the late C. Truesdell in his personal copy. It is annotated by W. Noll and by S. Antman who describe the monograph’s genesis and the impact it has made on the modern development of mechanics. Originally published as Volume III/3 of the famous Encyclopedia of Physics in 1965, this book describes and summarizes "everything that was both known and worth knowing in the field at the time." It also greatly contributed to the unification and standardization of the concepts, terms and notations in the field.
Advanced Continuum Theories And Finite Element Analyses
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Author : James D Lee
language : en
Publisher: World Scientific
Release Date : 2020-01-08
Advanced Continuum Theories And Finite Element Analyses written by James D Lee and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-08 with Technology & Engineering categories.
This comprehensive volume presents a unified framework of continuum theories. It indicates that (i) microcontinuum theories (micromorphic and micropolar theories) are natural extension of classical continuum mechanics, and (ii) classical continuum mechanics is a special case of microcontinuum theories when the deformable material point is idealized as a single mathematical point. The kinematics and basic laws are rigorously derived. Based on axiomatic approach, constitutive theory is systematically derived for various kinds of materials, ranging from Stokesian fluid to thermo-visco-elastic-plastic solid. Material force and Thermomechanical-electromagnetic coupling are introduced and discussed. Moreover, general finite element methods for large-strain thermomechanical coupling physical phenomena are systematically formulated. Also, non-classical continuum theories (Nonlocal Theory, Mechanobiology, 4D printing, Poromechanics, and Non-Self-Similar Crack Propagation) are rigorously formulated with applications and demonstrated numerically.As an advanced monograph, this unique compendium can also be used as a textbook for several graduate courses, including continuum mechanics, finite element methods, and advanced engineering science theories. Extensive problems are provided to help students to better understand the topics covered.
Microcontinuum Field Theories
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Author : A. Cemal Eringen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Microcontinuum Field Theories written by A. Cemal Eringen 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 2012-12-06 with Science categories.
Microcontinuum field theories constitute an extension of classical field theories -- of elastic bodies, deformations, electromagnetism, and the like -- to microscopic spaces and short time scales. Material bodies are here viewed as collections of large numbers of deformable particles, much as each volume element of a fluid in statistical mechanics is viewed as consisting of a large number of small particles for which statistical laws are valid. Classical continuum theories are valid when the characteristic length associated with external forces or stimuli is much larger than any internal scale of the body under consideration. When the characteristic lengths are comparable, however, the response of the individual constituents becomes important, for example, in considering the fluid or elastic properties of blood, porous media, polymers, liquid crystals, slurries, and composite materials. This volume is concerned with the kinematics of microcontinua. It begins with a discussion of strain, stress tensors, balance laws, and constitutive equations, and then discusses applications of the fundamental ideas to the theory of elasticity.
Computational Methods Based On Peridynamics And Nonlocal Operators
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Author : Timon Rabczuk
language : en
Publisher: Springer Nature
Release Date : 2023-02-15
Computational Methods Based On Peridynamics And Nonlocal Operators written by Timon Rabczuk and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-15 with Technology & Engineering categories.
This book provides an overview of computational methods based on peridynamics and nonlocal operators and their application to challenging numerical problems which are difficult to deal with traditional methods such as the finite element method, material failure being “only” one of them. The authors have also developed a higher-order nonlocal operator approaches capable of solving higher-order partial differential equations on arbitrary domains in higher-dimensional space with ease. This book is of interest to those in academia and industry.
Size Dependent Continuum Mechanics Approaches
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Author : Esmaeal Ghavanloo
language : en
Publisher: Springer Nature
Release Date : 2021-04-02
Size Dependent Continuum Mechanics Approaches written by Esmaeal Ghavanloo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-02 with Science categories.
This book offers a comprehensive and timely report of size-dependent continuum mechanics approaches. Written by scientists with worldwide reputation and established expertise, it covers the most recent findings, advanced theoretical developments and computational techniques, as well as a range of applications, in the field of nonlocal continuum mechanics. Chapters are concerned with lattice-based nonlocal models, Eringen’s nonlocal models, gradient theories of elasticity, strain- and stress-driven nonlocal models, and peridynamic theory, among other topics. This book provides researchers and practitioners with extensive and specialized information on cutting-edge theories and methods, innovative solutions to current problems and a timely insight into the behavior of some advanced materials and structures. It also offers a useful reference guide to senior undergraduate and graduate students in mechanical engineering, materials science, and applied physics.
Electrodynamics Of Continua I
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Author : A. Cemal Eringen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Electrodynamics Of Continua I written by A. Cemal Eringen 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 2012-12-06 with Science categories.
The electrodynamics of continua is a branch ofthe physical sciences concerned with the interaction of electromagnetic fields with deformable bodies. De formable bodies are considered to be continua endowed with continuous distributions of mass and charge. The theory of electromagnetic continua is concerned with the determination of deformations, motions, stress, and elec tromagnetic fields developed in bodies upon the applications of external loads. External loads may be of mechanical origin (e.g., forces, couples, constraints placed on the surface of the body, and initial and boundary conditions arising from thermal and other changes) and/or electromagnetic origin (e.g., electric, magnetic, and current fields). Because bodies of different constitutions respond to external stimuli in a different way, it is imperative to characterize properly the response functions relevant to a given class of continua. This is done by means of the constitutive theory. For example, an elastic dielectric responds to electromagnetic fields in a totally different way than a magnetic fluid. The present book is intended to present a unified approach to the subject matter, based on the principles of contemporary continuum physics.
Theories And Analyses Of Beams And Axisymmetric Circular Plates
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Author : J N Reddy
language : en
Publisher: CRC Press
Release Date : 2022-06-30
Theories And Analyses Of Beams And Axisymmetric Circular Plates written by J N Reddy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-30 with Technology & Engineering categories.
This comprehensive textbook compiles cutting-edge research on beams and circular plates, covering theories, analytical solutions, and numerical solutions of interest to students, researchers, and engineers working in industry. Detailing both classical and shear deformation theories, the book provides a complete study of beam and plate theories, their analytical (exact) solutions, variational solutions, and numerical solutions using the finite element method. Beams and plates are some of the most common structural elements used in many engineering structures. The book details both classical and advanced (i.e., shear deformation) theories, scaling in complexity to aid the reader in self-study, or to correspond with a taught course. It covers topics including equations of elasticity, equations of motion of the classical and first-order shear deformation theories, and analytical solutions for bending, buckling, and natural vibration. Additionally, it details static as well as transient response based on exact, the Navier, and variational solution approaches for beams and axisymmetric circular plates, and has dedicated chapters on linear and nonlinear finite element analysis of beams and circular plates. Theories and Analyses of Beams and Axisymmetric Circular Plates will be of interest to aerospace, civil, materials, and mechanical engineers, alongside students and researchers in solid and structural mechanics.