Continuum Theory

Author : A. Cemal Eringen
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 53,9 Mb
Release : 2007-06-14
Category : Science
ISBN : 9780387226439

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Nonlocal Continuum Field Theories by A. Cemal Eringen Pdf

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.

Author : Wolfgang H. Müller
Publisher : Springer Science & Business Media
Page : 399 pages
File Size : 42,9 Mb
Release : 2014-01-18
Category : Technology & Engineering
ISBN : 9789400777996

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An Expedition to Continuum Theory by Wolfgang H. Müller Pdf

This book introduces field theory as required in solid and fluid mechanics as well as in electromagnetism. It includes the necessary applied mathematical framework of tensor algebra and tensor calculus, using an inductive approach particularly suited to beginners. It is geared toward undergraduate classes in continuum theory for engineers in general, and more specifically to courses in continuum mechanics. Students will gain a sound basic understanding of the subject as well as the ability to solve engineering problems by applying the general laws of nature in terms of the balances for mass, momentum, and energy in combination with material-specific relations in terms of constitutive equations, thus learning how to use the theory in practice for themselves. This is facilitated by numerous examples and problems provided throughout the text.

Author : Peter Haupt
Publisher : Springer Science & Business Media
Page : 666 pages
File Size : 44,5 Mb
Release : 2013-03-14
Category : Technology & Engineering
ISBN : 9783662047750

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Continuum Mechanics and Theory of Materials by Peter Haupt Pdf

The new edition includes additional analytical methods in the classical theory of viscoelasticity. This leads to a new theory of finite linear viscoelasticity of incompressible isotropic materials. Anisotropic viscoplasticity is completely reformulated and extended to a general constitutive theory that covers crystal plasticity as a special case.

Author : Sam Nadler
Publisher : CRC Press
Page : 349 pages
File Size : 48,7 Mb
Release : 2017-07-12
Category : Mathematics
ISBN : 9781482277166

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Continuum Theory by Sam Nadler Pdf

A textbook for either a semester or year course for graduate students of mathematics who have had at least one course in topology. Introduces continuum theory through a combination of classical and modern techniques. Annotation copyright Book News, Inc. Portland, Or.

Author : Paul J. Cohen
Publisher : Courier Corporation
Page : 196 pages
File Size : 45,8 Mb
Release : 2008-12-09
Category : Mathematics
ISBN : 9780486469218

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Set Theory and the Continuum Hypothesis by Paul J. Cohen Pdf

This exploration of a notorious mathematical problem is the work of the man who discovered the solution. Written by an award-winning professor at Stanford University, it employs intuitive explanations as well as detailed mathematical proofs in a self-contained treatment. This unique text and reference is suitable for students and professionals. 1966 edition. Copyright renewed 1994.

Author : A.J.M. Spencer
Publisher : Springer
Page : 290 pages
File Size : 50,7 Mb
Release : 2014-05-04
Category : Science
ISBN : 9783709143360

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Continuum Theory of the Mechanics of Fibre-Reinforced Composites by A.J.M. Spencer Pdf

Author : W. Noll,R. A. Toupin,C. C. Wang
Publisher : Springer Science & Business Media
Page : 187 pages
File Size : 52,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642859922

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Continuum Theory of Inhomogeneities in Simple Bodies by W. Noll,R. A. Toupin,C. C. Wang Pdf

The term "dislocation" is used in several different senses in the literature of mechanics. In the elassic work of VOLTERRA, WEINGARTEN, and SOMIGLIANA, it refers to particular solutions of the equations of linear elasticity, in which a con tinuous field of strain does not correspond, globally, to a continuous field of dis placement. The configuration of the body so obtained, even when that body is free of all load, is subject to interior stress that does not vanish, and in general no deformation of the body as a wh oIe can bring it into a stress-free configuration. Nevertheless, if any sufficiently sm all part of the body is considered by itself, a configuration for it in which the stress is everywhere zero may be found at once. In this work constitutiL"e assumptions provide the basic data. These consist in prescribed stress-free configurations for each material point and in prescribed elastic moduli governing the response to deformation from the stress-free configuration at each material point. Everything follows from these data, ineluding the dislocations present, if any. In particular, the common boundary-value problems of linear elasticity may be set and solved for the dislocated body.

Author : John M. Ball,David Kinderlehrer,Paulo Podio-Guidugli,Marshall Slemrod
Publisher : Springer Science & Business Media
Page : 477 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642599385

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Fundamental Contributions to the Continuum Theory of Evolving Phase Interfaces in Solids by John M. Ball,David Kinderlehrer,Paulo Podio-Guidugli,Marshall Slemrod Pdf

A traditional way to honor distinguished scientists is to combine collections of papers solicited from friendly colleagues into dedicatory volumes. To honor our friend and colleague Mort Gurtin on the occasion of his sixty-fifth birthday, we followed a surer path to produce a work of intrinsic and lasting scientific value: We collected pa pers that we deemed seminal in the field of evolving phase interfaces in solids, a field to which Mort Gurtin himself has made fundamental contributions. Our failure for lack of space to include in this volume every paper of major significance is mitigated by the ma gisterial introduction prepared by Eliot Fried, which assesses the contributions of nu merous works. We hope that this collection will prove useful and stimulating to both researchers and students in this exciting field. August 1998 JohnM. Ball David Kinderlehrer Paulo Podio-Guidugli Marshall Slemrod Contents Introduction: Fifty Years of Research on Evolving Phase Interfaces By Eliot Fried. 0 •••••••••••••••••••••••••••••••••••••••••••••••• 0 ••••• 1 I. Papers on Materials Science Surface Tension as a Motivation for Sintering By C. Herring 33 Two-Dimensional Motion of Idealized Grain Boundaries By W. W. Mullins 0 ••••••••••• 0 ••••••••••••••••••• 70 Morphological. Stability of a Particle Growing by Diffusion or Heat Flow By w. w. Mullins and R. F. Sekerka 75 Energy Relations and the Energy-Momentum Tensor in Continuum Mechanics By J. D. Eshelby 82 The Interactions of Composition and Stress in Crystalline Solids By F. e. Larche and 1. W. Cahn 120 II.

Author : Raymond M. Smullyan,Melvin Fitting
Publisher : Unknown
Page : 0 pages
File Size : 53,9 Mb
Release : 2010
Category : Continuum hypothesis
ISBN : 0486474844

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Set Theory and the Continuum Problem by Raymond M. Smullyan,Melvin Fitting Pdf

A lucid, elegant, and complete survey of set theory, this three-part treatment explores axiomatic set theory, the consistency of the continuum hypothesis, and forcing and independence results. 1996 edition.

Author : Akhtar S. Khan,Sujian Huang
Publisher : John Wiley & Sons
Page : 434 pages
File Size : 50,8 Mb
Release : 1995-02-28
Category : Science
ISBN : 0471310433

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Continuum Theory of Plasticity by Akhtar S. Khan,Sujian Huang Pdf

The only modern, up-to-date introduction to plasticity Despite phenomenal progress in plasticity research over the past fifty years, introductory books on plasticity have changed very little. To meet the need for an up-to-date introduction to the field, Akhtar S. Khan and Sujian Huang have written Continuum Theory of Plasticity--a truly modern text which offers a continuum mechanics approach as well as a lucid presentation of the essential classical contributions. The early chapters give the reader a review of elementary concepts of plasticity, the necessary background material on continuum mechanics, and a discussion of the classical theory of plasticity. Recent developments in the field are then explored in sections on the Mroz Multisurface model, the Dafalias and Popov Two Surface model, the non-linear kinematic hardening model, the endochronic theory of plasticity, and numerous topics in finite deformation plasticity theory and strain space formulation for plastic deformation. Final chapters introduce the fundamentals of the micromechanics of plastic deformation and the analytical coupling between deformation of individual crystals and macroscopic material response of the polycrystal aggregate. For graduate students and researchers in engineering mechanics, mechanical, civil, and aerospace engineering, Continuum Theory of Plasticity offers a modern, comprehensive introduction to the entire subject of plasticity.

Author : Attila Askar
Publisher : World Scientific
Page : 208 pages
File Size : 55,5 Mb
Release : 1986-07-01
Category : Electronic
ISBN : 9789814518956

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Lattice Dynamical Foundations Of Continuum Theories: Elasticity, Piezoelectricity, Viscoelasticity, Plasticity by Attila Askar Pdf

This book presents a discussion of lattice dynamics for perfect and imperfect lattices and their relation to continuum theories of elasticity, piezoelectricity, viscoelasticity and plasticity. Some of the material is rather classical and close in spirit to solid state physics. A major aim here is to present a coherent theory for the four basic behavior types in the style of continuum mechanics. In each case, emphasis is on an explicit display of the physical mechanisms involved rather than general formalisms. The material is presented in terms of an atomistic picture for the discrete system. The basic ideas are believed to be relevant also at an intermediate scale in the continuum description of media with structure such as granular materials and composites.

Author : Haim Judah,Winfried Just,Hugh Woodin
Publisher : Springer Science & Business Media
Page : 417 pages
File Size : 50,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461397540

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Set Theory of the Continuum by Haim Judah,Winfried Just,Hugh Woodin Pdf

Primarily consisting of talks presented at a workshop at the MSRI during its "Logic Year" 1989-90, this volume is intended to reflect the whole spectrum of activities in set theory. The first section of the book comprises the invited papers surveying the state of the art in a wide range of topics of set-theoretic research. The second section includes research papers on various aspects of set theory and its relation to algebra and topology. Contributors include: J.Bagaria, T. Bartoszynski, H. Becker, P. Dehornoy, Q. Feng, M. Foreman, M. Gitik, L. Harrington, S. Jackson, H. Judah, W. Just, A.S. Kechris, A. Louveau, S. MacLane, M. Magidor, A.R.D. Mathias, G. Melles, W.J. Mitchell, S. Shelah, R.A. Shore, R.I. Soare, L.J. Stanley, B. Velikovic, H. Woodin.

Author : Christina Papenfuß
Publisher : Springer Nature
Page : 238 pages
File Size : 41,5 Mb
Release : 2020-05-16
Category : Science
ISBN : 9783030439897

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Continuum Thermodynamics and Constitutive Theory by Christina Papenfuß Pdf

This book presents different thermodynamic approaches in the area of constitutive theory: thermodynamics of irreversible processes, rational thermodynamics, and extended thermodynamics. These different approaches are analyzed with respect to their presuppositions, as well as to their results, and each method is applied to several important examples. In many cases these examples are archetypes for numerous technologically important materials; i.e. complex materials having an internal structure. Some of the examples dealt with in this book are liquid crystals, colloid suspensions, ans fiber suspensions. The book well serves students and researchers who have basic knowledge in continuum mechanics and thermodynamics. It provides a systematic overview of the vast field of thermodynamic constitutive theory, beginning from a historical perspective and concluding with outstanding questions in recent research.

Author : P. Chadwick
Publisher : Courier Corporation
Page : 191 pages
File Size : 44,7 Mb
Release : 2012-08-08
Category : Science
ISBN : 9780486139142

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Continuum Mechanics by P. Chadwick Pdf

DIVComprehensive treatment offers 115 solved problems and exercises to promote understanding of vector and tensor theory, basic kinematics, balance laws, field equations, jump conditions, and constitutive equations. /div

Author : W Michael Lai,David Rubin,Erhard Krempl
Publisher : Butterworth-Heinemann
Page : 549 pages
File Size : 54,6 Mb
Release : 2009-07-23
Category : Science
ISBN : 9780080942520

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Introduction to Continuum Mechanics by W Michael Lai,David Rubin,Erhard Krempl Pdf

Continuum Mechanics is a branch of physical mechanics that describes the macroscopic mechanical behavior of solid or fluid materials considered to be continuously distributed. It is fundamental to the fields of civil, mechanical, chemical and bioengineering. This time-tested text has been used for over 35 years to introduce junior and senior-level undergraduate engineering students, as well as graduate students, to the basic principles of continuum mechanics and their applications to real engineering problems. The text begins with a detailed presentation of the coordinate invariant quantity, the tensor, introduced as a linear transformation. This is then followed by the formulation of the kinematics of deformation, large as well as very small, the description of stresses and the basic laws of continuum mechanics. As applications of these laws, the behaviors of certain material idealizations (models) including the elastic, viscous and viscoelastic materials, are presented. This new edition offers expanded coverage of the subject matter both in terms of details and contents, providing greater flexibility for either a one or two-semester course in either continuum mechanics or elasticity. Although this current edition has expanded the coverage of the subject matter, it nevertheless uses the same approach as that in the earlier editions - that one can cover advanced topics in an elementary way that go from simple to complex, using a wealth of illustrative examples and problems. It is, and will remain, one of the most accessible textbooks on this challenging engineering subject. Significantly expanded coverage of elasticity in Chapter 5, including solutions of some 3-D problems based on the fundamental potential functions approach New section at the end of Chapter 4 devoted to the integral formulation of the field equations Seven new appendices appear at the end of the relevant chapters to help make each chapter more self-contained Expanded and improved problem sets providing both intellectual challenges and engineering applications