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Nonlocal Continuum Field Theories
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Book Synopsis Nonlocal Continuum Field Theories by : A. Cemal Eringen
Download or read book Nonlocal Continuum Field Theories written by A. Cemal Eringen and published by Springer Science & Business Media. This book was released on 2007-06-14 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Continuum Physics by : A. Cemal Eringen
Download or read book Continuum Physics written by A. Cemal Eringen and published by Elsevier. This book was released on 2012-12-02 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuum Physics, Volume IV: Polar and Nonlocal Field Theories discusses the exposition of field theories for bodies which possess inner structure that can interact with mechanical and electromagnetic fields. This book provides precise presentations of exact continuum theories on materially non-uniform or non-simple bodies that can respond to short- and long-range inter-particle loads and fields. This volume consists of three parts. Part I is devoted to the study of continuum field theories for bodies having inner structure. All materials, to some extent, are composed of particles that behave like small rigid bodies or deformable particles, unlike the geometrical points of the classical continuum theory. The developments of nonlocal theories of nonpolar and polar continua are covered in Parts II and III. This publication is valuable to students and researchers interested in polar and nonlocal field theories.
Book Synopsis Continuum Physics: Polar and non-local field theories by : A. Cemal Eringen
Download or read book Continuum Physics: Polar and non-local field theories written by A. Cemal Eringen and published by . This book was released on 1971 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlocal Continuum Limits of p-Laplacian Problems on Graphs by : Imad El Bouchairi
Download or read book Nonlocal Continuum Limits of p-Laplacian Problems on Graphs written by Imad El Bouchairi and published by Cambridge University Press. This book was released on 2023-04-30 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Size-Dependent Continuum Mechanics Approaches by : Esmaeal Ghavanloo
Download or read book Size-Dependent Continuum Mechanics Approaches written by Esmaeal Ghavanloo and published by Springer Nature. This book was released on 2021-04-02 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Non-Classical Continuum Mechanics by : Gérard A. Maugin
Download or read book Non-Classical Continuum Mechanics written by Gérard A. Maugin and published by Springer. This book was released on 2016-09-24 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dictionary offers clear and reliable explanations of over 100 keywords covering the entire field of non-classical continuum mechanics and generalized mechanics, including the theory of elasticity, heat conduction, thermodynamic and electromagnetic continua, as well as applied mathematics. Every entry includes the historical background and the underlying theory, basic equations and typical applications. The reference list for each entry provides a link to the original articles and the most important in-depth theoretical works. Last but not least, ever y entry is followed by a cross-reference to other related subject entries in the dictionary.
Book Synopsis Microcontinuum Field Theories by : A. Cemal Eringen
Download or read book Microcontinuum Field Theories written by A. Cemal Eringen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Microcontinuum field theories extend classical field theories to microscopic spaces and short time scales. 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. The ideas developed here are important in modeling the fluid or elastic properties of porous media, polymers, liquid crystals, slurries, and composite materials.
Book Synopsis Nonlocal Quantum Field Theory and Stochastic Quantum Mechanics by : K.H. Namsrai
Download or read book Nonlocal Quantum Field Theory and Stochastic Quantum Mechanics written by K.H. Namsrai and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: over this stochastic space-time leads to the non local fields considered by G. V. Efimov. In other words, stochasticity of space-time (after being averaged on a large scale) as a self-memory makes the theory nonlocal. This allows one to consider in a unified way the effect of stochasticity (or nonlocality) in all physical processes. Moreover, the universal character of this hypothesis of space-time at small distances enables us to re-interpret the dynamics of stochastic particles and to study some important problems of the theory of stochastic processes [such as the relativistic description of diffusion, Feynman type processes, and the problem of the origin of self-turbulence in the motion of free particles within nonlinear (stochastic) mechanics]. In this direction our approach (Part II) may be useful in recent developments of the stochastic interpretation of quantum mechanics and fields due to E. Nelson, D. Kershaw, I. Fenyes, F. Guerra, de la Pena-Auerbach, J. -P. Vigier, M. Davidson, and others. In particular, as shown by N. Cufaro Petroni and J. -P. Vigier, within the discussed approach, a causal action-at-distance interpretation of a series of experiments by A. Aspect and his co-workers indicating a possible non locality property of quantum mechanics, may also be obtained. Aspect's results have recently inspired a great interest in different nonlocal theories and models devoted to an understanding of the implications of this nonlocality. This book consists of two parts.
Book Synopsis Computational Continuum Mechanics of Nanoscopic Structures by : Esmaeal Ghavanloo
Download or read book Computational Continuum Mechanics of Nanoscopic Structures written by Esmaeal Ghavanloo and published by Springer. This book was released on 2019-02-19 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive treatment of nonlocal elasticity theory as applied to the prediction of the mechanical characteristics of various types of biological and non-biological nanoscopic structures with different morphologies and functional behaviour. It combines fundamental notions and advanced concepts, covering both the theory of nonlocal elasticity and the mechanics of nanoscopic structures and systems. By reporting on recent findings and discussing future challenges, the book seeks to foster the application of nonlocal elasticity based approaches to the emerging fields of nanoscience and nanotechnology. It is a self-contained guide, and covers all relevant background information, the requisite mathematical and computational techniques, theoretical assumptions, physical methods and possible limitations of the nonlocal approach, including some practical applications. Mainly written for researchers in the fields of physics, biophysics, mechanics, and nanoscience, as well as computational engineers, the book can also be used as a reference guide for senior undergraduate and graduate students, as well as practicing engineers working in a range of areas, such as computational condensed matter physics, computational materials science, computational nanoscience and nanotechnology, and nanomechanics.
Book Synopsis Computational Methods Based on Peridynamics and Nonlocal Operators by : Timon Rabczuk
Download or read book Computational Methods Based on Peridynamics and Nonlocal Operators written by Timon Rabczuk and published by Springer Nature. This book was released on 2023-02-15 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis 50+ Years of AIMETA by : Giuseppe Rega
Download or read book 50+ Years of AIMETA written by Giuseppe Rega and published by Springer Nature. This book was released on 2022-06-04 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book retraces the history of the Italian Association of Theoretical and Applied Mechanics (AIMETA) since its establishment in 1965. AIMETA is the official Italian association of mechanics adhering to IUTAM (International Union of Theoretical and Applied Mechanics), which organizes and coordinates a meaningful number of research activities, the most important of which are the biennial National Congress and the internationally renowned journal “Meccanica”, published by Springer. Besides collecting and organizing all related important data and information, as far as possible, by distinguishing among the five scientific areas – general mechanics, solids, structures, fluids, machines – encompassed by AIMETA, the history of the association is assumed as a proper perspective to overview the evolution of theoretical and applied mechanics in Italy over about the last fifty years. This is accomplished in the first part of the book. with also a specific focus on the mechanics of solids and structures, where the biographies of a meaningful number of recognized Italian scholars of mechanics in all areas are also provided, along with testimonials and memories by a few senior people meaningfully involved with AIMETA and Italian mechanics. The second part gives an account, although unavoidably incomplete, of recent developments of mechanical sciences in Italy, as reflected also in the activities of AIMETA and with reference to the international context. Contributions by a number of invited senior scholars, still very active, consist of overviews on some scientific themes in the various areas, summaries of achievements of research groups, expressions of research viewpoints, prospects for future developments.
Book Synopsis Electrodynamics of Continua II by : A.Cemal Eringen
Download or read book Electrodynamics of Continua II written by A.Cemal Eringen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume of a two-volume set presenting a unified approach to the electrodynamics of continua, based on the principles of contemporary continuum of physics. The first volume was devoted mainly to the development of the theory and applications to deformable solid media. This volume extends the developments of the first volume to richer and newer grounds. It contains discussions on fluid media, magnetohydrodynamics, eletrohydrodynamics and media with more complicated structures. With the discussion, in the last two chapters, of memory-dependent materials and non-local E-M theory, the authors account for the nonlocal effects arising from motions and fields of material points at past times and at spatially distant points. This discussion is included here to stimulate further research in these important fields, which are presently in development stages. The second volume is self-contained and can be studied without the help of volume I. A section summarizing the constitutive equations and the underlying physical ideas, which were presented in more detail in the first volume, is included. This volume may be used as a basis for several graduate courses in engineering schools, applied mathematics and physics departments. It also contains fresh ideas and will stimulate further research in the directions the authors outline.
Book Synopsis Electrodynamics of Continua I by : A. Cemal Eringen
Download or read book Electrodynamics of Continua I written by A. Cemal Eringen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Continuum Mechanics Through the Twentieth Century by : Gerard A Maugin
Download or read book Continuum Mechanics Through the Twentieth Century written by Gerard A Maugin and published by Springer Science & Business Media. This book was released on 2013-04-08 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This overview of the development of continuum mechanics throughout the twentieth century is unique and ambitious. Utilizing a historical perspective, it combines an exposition on the technical progress made in the field and a marked interest in the role played by remarkable individuals and scientific schools and institutions on a rapidly evolving social background. It underlines the newly raised technical questions and their answers, and the ongoing reflections on the bases of continuum mechanics associated, or in competition, with other branches of the physical sciences, including thermodynamics. The emphasis is placed on the development of a more realistic modeling of deformable solids and the exploitation of new mathematical tools. The book presents a balanced appraisal of advances made in various parts of the world. The author contributes his technical expertise, personal recollections, and international experience to this general overview, which is very informative albeit concise.
Book Synopsis Continuum Mechanics of Single-Substance Bodies by : A. Cemal Eringen
Download or read book Continuum Mechanics of Single-Substance Bodies written by A. Cemal Eringen and published by Academic Press. This book was released on 2016-11-08 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuum Physics, Volume II: Continuum Mechanics of Single-Substance Bodies discusses the continuum mechanics of bodies constituted by a single substance, providing a thorough and precise presentation of exact theories that have evolved during the past years. This book consists of three parts—basic principles, constitutive equations for simple materials, and methods of solution. Part I of this publication is devoted to a discussion of basic principles irrespective of material geometry and constitution that are valid for all kinds of substances, including composites. The geometrical notions, kinematics, balance laws, and thermodynamics of continua are also deliberated. Part II focuses on materials consisting of a single substance, followed by a general theory of constitutive equations and special types of bodies. The thermoelastic solids, thermoviscous fluids, and memory-dependent materials are likewise considered. Part III is devoted to a discussion of a variety of nonlinear and linear problems, as well as nonlinear deformations of elastic solids, viscometric fluids, singular surfaces and waves, and complex function technique. This volume is a good source for researchers and students conducting work on the continuum mechanics of single-substance bodies.
Book Synopsis Applications Of Tensor Analysis In Continuum Mechanics by : Michael J Cloud
Download or read book Applications Of Tensor Analysis In Continuum Mechanics written by Michael J Cloud and published by World Scientific. This book was released on 2018-07-10 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'A strong point of this book is its coverage of tensor theory, which is herein deemed both more readable and more substantial than many other historic continuum mechanics books. The book is self-contained. It serves admirably as a reference resource on fundamental principles and equations of tensor mathematics applied to continuum mechanics. Exercises and problem sets are useful for teaching … The book is highly recommended as both a graduate textbook and a reference work for students and more senior researchers involved in theoretical and mathematical modelling of continuum mechanics of materials. Key concepts are well described in the text and are supplemented by informative exercises and problem sets with solutions, and comprehensive Appendices provide important equations for ease of reference.'Contemporary PhysicsA tensor field is a tensor-valued function of position in space. The use of tensor fields allows us to present physical laws in a clear, compact form. A byproduct is a set of simple and clear rules for the representation of vector differential operators such as gradient, divergence, and Laplacian in curvilinear coordinate systems. The tensorial nature of a quantity permits us to formulate transformation rules for its components under a change of basis. These rules are relatively simple and easily grasped by any engineering student familiar with matrix operators in linear algebra. More complex problems arise when one considers the tensor fields that describe continuum bodies. In this case general curvilinear coordinates become necessary. The principal basis of a curvilinear system is constructed as a set of vectors tangent to the coordinate lines. Another basis, called the dual basis, is also constructed in a special manner. The existence of these two bases is responsible for the mysterious covariant and contravariant terminology encountered in tensor discussions.This book provides a clear, concise, and self-contained treatment of tensors and tensor fields. It covers the foundations of linear elasticity, shell theory, and generalized continuum media, offers hints, answers, and full solutions for many of the problems and exercises, and Includes a handbook-style summary of important tensor formulas.The book can be useful for beginners who are interested in the basics of tensor calculus. It also can be used by experienced readers who seek a comprehensive review on applications of the tensor calculus in mechanics.
Book Synopsis New Advances in Materials Technologies by : Hossein Hariri Asli
Download or read book New Advances in Materials Technologies written by Hossein Hariri Asli and published by CRC Press. This book was released on 2024-06-28 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new volume examines the mathematical and experimental methods for advanced engineering materials and structures. It also helps to determine practical applications under a wide range of conditions, helping to set up what is needed to produce a new generation of new materials. The diversity of such mathematical models and experimental methods applied for different types of advanced materials and structures and their behavior is highlighted in this volume. The subjects covered in this book include geospatial information systems (GIS) and networked sensors modeling, mathematical modeling in fluid and solid mechanics, deformations in a nonlocal isotropic thermoelastic materials, optical properties of solid materials, nanoscale and modern energy materials and devices, smart materials-based E-nose technology, and more. New Advances in Materials Technologies: Experimental Characterizations, Theoretical Modeling and Field Practices is an essential reference that will be useful for researchers who specialize in advanced materials and structures, experimental mechanics of materials, mathematical modeling, and related fields of applied mathematics. This book is also suitable for post-graduate engineering students who need to have an overview on applied in mechanics of materials.
