Nonlocal Continuum Field Theories / Edition 1

Nonlocal Continuum Field Theories / Edition 1

by A. Cemal Eringen
     
 

ISBN-10: 0387952756

ISBN-13: 9780387952758

Pub. Date: 06/14/2002

Publisher: Springer New York

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…  See more details below

Overview

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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Product Details

ISBN-13:
9780387952758
Publisher:
Springer New York
Publication date:
06/14/2002
Edition description:
2002
Pages:
376
Product dimensions:
6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

Preface
Introduction
1Motion and Deformation1
2Stress15
3Constitutive Equations31
4Nonlocal Electromagnetic Theory49
5Constitutive Equations of Nonlocal Electromagnetic Media61
6Nonlocal Linear Elasticity71
7Nonlocal Fluid Dynamics177
8Nonlocal Linear Electromagnetic Theory193
9Memory-Dependent Nonlocal Thermoelastic Solids223
10Memory-Dependent Nonlocal Fluids231
11Memory-Dependent Nonlocal E-M Elastic Solids237
12Memory-Dependent Nonlocal E-M Thermofluids247
13Nonlocal Microcontinua253
14Memory-Dependent Nonlocal E-M Elastic Solids325
15Nonlocal Continuum Theory of Liquid Crystals337
App. A351
References357
Index365
Errata375

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