Nonlocal Continuum Field Theories / Edition 1

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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.

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Editorial Reviews

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From the reviews:

"The volume Nonlocal continuum field theories concentrates on the formulation of nonlocal balance and constitutive equations in the context of mechanics, but also of electromagnetic theory. … it is clear that Eringen’s latest book is a fascinating and stimulating one that should have a dedicated place on the shelf of every researcher in physics, mechanics or materials science." (Technische Mechanik, Vol. 25 (1), 2005)

"This book is … an organized presentation of the numerous successful achievements of its author in the nonlocal theories of elasticity, fluid mechanics and electromagnetism … . With the large spectrum of problems approached and the many questions it still raises on the foundations of continuum physics, it clearly belongs to the shelves of all scholars in generalized continuum mechanics and all those interested in further developments bridging different scales of apprehending the physical world." (Gérard A. Maugin, Mathematical Reviews, Issue 2003 m)

"This interesting book covers a gap in the literature on continuum field theories. It contains and updates the own research of the author and his collaborators for almost the last forty years. … The purpose of the book is to present a unified approach to the formulations of nonlocal field theories … . Every chapter ends with an interesting collection of problems." (Manuel de León, Zentralblatt MATH, Vol. 1023, 2003)

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Product Details

  • ISBN-13: 9780387952758
  • Publisher: Springer New York
  • Publication date: 6/14/2002
  • Edition description: 2002
  • Edition number: 1
  • Pages: 376
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.88 (d)

Table of Contents

1 Motion and Deformation 1
2 Stress 15
3 Constitutive Equations 31
4 Nonlocal Electromagnetic Theory 49
5 Constitutive Equations of Nonlocal Electromagnetic Media 61
6 Nonlocal Linear Elasticity 71
7 Nonlocal Fluid Dynamics 177
8 Nonlocal Linear Electromagnetic Theory 193
9 Memory-Dependent Nonlocal Thermoelastic Solids 223
10 Memory-Dependent Nonlocal Fluids 231
11 Memory-Dependent Nonlocal E-M Elastic Solids 237
12 Memory-Dependent Nonlocal E-M Thermofluids 247
13 Nonlocal Microcontinua 253
14 Memory-Dependent Nonlocal E-M Elastic Solids 325
15 Nonlocal Continuum Theory of Liquid Crystals 337
App. A 351
References 357
Index 365
Errata 375
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