Nonlocal Continuum Field Theories

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 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.

List of contents

Motion and Deformation.- Stress.- Constitutive Equations.- Nonlocal Electromagnetic Theory.- Constitutive Equations of Nonlocal Electromagnetic Media.- Nonlocal Linear Elasticity.- Nonlocal Fluid Dynamics.- Nonlocal Linear Electromagnetic Theory.- Memory-Dependent Nonlocal Thermoelastic Solids.- Memory-Dependent Nonlocal Fluids.- Memory-Dependent Nonlocal Electromagnetic Elastic Solids.- Memory-Dependent Nonlocal Electromagnetic Thermofluids.- Nonlocal Microcontinua.- Memory-Dependent Nonlocal Micropolar Electromagnetic Elastic Solids.- Nonlocal Continuum Theory of Liquid Crystals.

Summary

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.

Additional text

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)

Report

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)

Product details

• Authors: A Cemal Eringen, A. C. Eringen, A. Cemal Eringen
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 26.10.2010
• EAN: 9781441929310
• ISBN: 978-1-4419-2931-0
• No. of pages: 376
• Dimensions: 157 mm x 236 mm x 24 mm
• Weight: 599 g
• Illustrations: XVI, 376 p.
• Subjects: Natural sciences, medicine, IT, technology > Physics, astronomy > Atomic physics, nuclear physics; C, Classical mechanics, Theoretical and Applied Mechanics, Condensed Matter Physics, Condensed matter, Physics and Astronomy, Mechanics, Mechanics of solids, Mechanics, Applied, Engineering Mechanics