Nonlocal Continuum Field Theories 2002nd Edition by A. Cemal Eringen (PDF)

Description

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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⭐Excluding quantum effects and elementary particles physics, there exist, presently, two fundamental physical models that provide foundations for all physical theories : discrete (atomic) models and continuum field theories. The success of booth models has been demonstrated and tested throughout the last decades in explaining and predicting diverse physical phenomena.There is no doubt that at the microscopic (atomic) level local continuum theories fail to apply. Thus a strong prejudice has been perpetrated against the classical continuum theories. With the rise of polar and nonlocal theories, strong indications are at hand for booth the power and predictability of continuum models to assume an honorable place as physical theories.The primary purpose of this book is to illustrate this possibilty for a wide range of physical phenomena (dislocations, microcracks, fluid turbulence, crystals, inner structures, absorption of E-M waves, memory-depended thermoelastic solids, thermofluids, electromagnetic solids and fluids, etc.), while at the same time indicating the limitations of the theories. In fact, the aim is NOT a pontification of any model over the other but rather WHY BOOTH MODELS, ATOMIC AND CONTINUUM, ARE COMPLEMENTARY, and when used properly they bear fruits that cannot be harvested by means of either model alone.In spite of its age, the literature on nonlocal continuum field theories is not so extensive. There exist several reviews and papers, a few, and conference symposia, along with those of Eringen itself. This book presents a unification of these theories, but their formulation here in new and had not appeared before in the literature. In a sense this book is the “final” version of the work of the author and his collaborators.The text is well organized, and each chapter ends with a collection of problems. It is self contained :physical subjects are preceded by a brief introduction.This book is intended primarily for two audiences, first, the physics and engineering student, and second, the mathematics student. The only REAL prerequisities are BASIC mechanics and thermodynamics of continua, some undergraduate physics, and some familiarity with calculus of several variables. Most students have these by the beginning of the (first) graduate year.This is the latest book of Eringen, and a great companion to the other great book (in 2 volumes) of the author “Microcontinuum Field Theories” . It is a fascinating and stimulating one for every graduate student and scholar in physics and applied mathematics.

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