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Nonlocal Continuum Field Theories

  • Book
  • © 2002

Overview

Editors:
  1. A. Cemal Eringen

    1. Princeton University, Littleton, USA

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Motion and Deformation

    Pages 1-14

  3. Stress

    Pages 15-29

  4. Constitutive Equations

    Pages 31-48

  5. Nonlocal Electromagnetic Theory

    Pages 49-59

  6. Constitutive Equations of Nonlocal Electromagnetic Media

    Pages 61-70

  7. Nonlocal Linear Elasticity

    Pages 71-176

  8. Nonlocal Fluid Dynamics

    Pages 177-192

  9. Nonlocal Linear Electromagnetic Theory

    Pages 193-222

  10. Memory-Dependent Nonlocal Thermoelastic Solids

    Pages 223-229

  11. Memory-Dependent Nonlocal Fluids

    Pages 231-235

  12. Memory-Dependent Nonlocal Electromagnetic Elastic Solids

    Pages 237-245

  13. Memory-Dependent Nonlocal Electromagnetic Thermofluids

    Pages 247-252

  14. Nonlocal Microcontinua

    Pages 253-324

  15. Memory-Dependent Nonlocal Micropolar Electromagnetic Elastic Solids

    Pages 325-336

  16. Nonlocal Continuum Theory of Liquid Crystals

    Pages 337-356

  17. Back Matter

    Pages 357-376
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Keywords

About this book

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.

Reviews

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)

Editors and Affiliations

  • Princeton University, Littleton, USA

    A. Cemal Eringen

Bibliographic Information

  • Book Title: Nonlocal Continuum Field Theories

  • Editors: A. Cemal Eringen

  • DOI: https://doi.org/10.1007/b97697

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 2002

  • Hardcover ISBN: 978-0-387-95275-8Published: 14 June 2002

  • Softcover ISBN: 978-1-4419-2931-0Published: 03 December 2010

  • eBook ISBN: 978-0-387-22643-9Published: 14 June 2007

  • Edition Number: 1

  • Number of Pages: XVI, 376

  • Topics: Condensed Matter Physics, Theoretical and Applied Mechanics, Classical Mechanics

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