Continuum Physics
Continuum Physics

Author: Peter Hertel

Publisher: Springer Science & Business Media

Published: 2012-08-15

Total Pages: 293

ISBN-13: 3642295002

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This small book on the properties of continuously distributed matter covers a huge field. It sets out the governing principles of continuum physics and illustrates them by carefully chosen examples. These examples comprise structural mechanics and elasticity, fluid media, electricity and optics, thermoelectricity, fluctuation phenomena and more, from Archimedes' principle via Brownian motion to white dwarfs. Metamaterials, pattern formation by reaction-diffusion and surface plasmon polaritons are dealt with as well as classical topics such as Stokes' formula, beam bending and buckling, crystal optics and electro- and magnetooptic effects, dielectric waveguides, Ohm's law, surface acoustic waves, to mention just some. The set of balance equations for content, flow and production of particles, mass, charge, momentum, energy and entropy is augmented by material, or constitutive equations. They describe entire classes of materials, such as viscid fluids and gases, elastic media, dielectrics or electrical conductors. We discuss the response of matter to rapidly oscillating external parameters, in particular the electric field strength of light, in the framework of statistical thermodynamics. An appendix on fields and a glossary round off this bird's-eye view on continuum physics. /p Students of physics, engineering and related fields will benefit from the clear presentation of worked examples and the variety of solution methods, including numerical techniques. Lecturers or advanced students may profit from the unified view on a substantial part of physics. It may help them to embed their research field conceptually within a wider context.

Continuum Mechanics
Continuum Mechanics

Author: Peter Chadwick

Publisher: Courier Corporation

Published: 1999-01-01

Total Pages: 200

ISBN-13: 9780486401805

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Written in response to the dearth of practical and meaningful textbooks in the field of fundamental continuum mechanics, this comprehensive treatment offers students and instructors an immensely useful tool. Its 115 solved problems and exercises not only provide essential practice but also systematically advance the understanding of vector and tensor theory, basic kinematics, balance laws, field equations, jump conditions, and constitutive equations. Readers follow clear, formally precise steps through the central ideas of classical and modern continuum mechanics, expressed in a common, efficient notation that fosters quick comprehension and renders these concepts familiar when they reappear in other contexts. Completion of this brief course results in a unified basis for work in fluid dynamics and the mechanics of solid materials, a foundation of particular value to students of mathematics and physics, those studying continuum mechanics at an intermediate or advanced level, and postgraduate students in the applied sciences. "Should be excellent in its intended function as a problem book to accompany a lecture course." — Quarterly of Applied Math.

Continuum Mechanics and Thermodynamics
Continuum Mechanics and Thermodynamics

Author: Ellad B. Tadmor

Publisher: Cambridge University Press

Published: 2012

Total Pages: 373

ISBN-13: 1107008263

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Treats subjects directly related to nonlinear materials modeling for graduate students and researchers in physics, materials science, chemistry and engineering.

Continuum Mechanics and Theory of Materials
Continuum Mechanics and Theory of Materials

Author: Peter Haupt

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 666

ISBN-13: 3662047756

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The new edition includes additional analytical methods in the classical theory of viscoelasticity. This leads to a new theory of finite linear viscoelasticity of incompressible isotropic materials. Anisotropic viscoplasticity is completely reformulated and extended to a general constitutive theory that covers crystal plasticity as a special case.

Continuum Mechanics
Continuum Mechanics

Author: A. J. M. Spencer

Publisher: Courier Corporation

Published: 2012-06-08

Total Pages: 194

ISBN-13: 0486139476

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Undergraduate text offers an analysis of deformation and stress, covers laws of conservation of mass, momentum, and energy, and surveys the formulation of mechanical constitutive equations. 1992 edition.

A First Course in Continuum Mechanics
A First Course in Continuum Mechanics

Author: Oscar Gonzalez

Publisher: Cambridge University Press

Published: 2008-01-17

Total Pages: 5

ISBN-13: 0521886805

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The modeling and simulation of fluids, solids and other materials with significant coupling and thermal effects is becoming an increasingly important area of study in applied mathematics and engineering. Necessary for such studies is a fundamental understanding of the basic principles of continuum mechanics and thermodynamics. This book is a clear introduction to these principles. It is designed for a one- or two-quarter course for advanced undergraduate and beginning graduate students in the mathematical and engineering sciences, and is based on over nine years of teaching experience. It is also sufficiently self-contained for use outside a classroom environment. Prerequisites include a basic knowledge of linear algebra, multivariable calculus, differential equations and physics. The authors begin by explaining tensor algebra and calculus in three-dimensional Euclidean space. Using both index and coordinate-free notation, they introduce the basic axioms of continuum mechanics pertaining to mass, force, motion, temperature, energy and entropy, and the concepts of frame-indifference and material constraints. They devote four chapters to different theories of fluids and solids, and, unusually at this level, they consider both isothermal and thermal theories in detail. The book contains a wealth of exercises that support the theory and illustrate various applications. Full solutions to odd-numbered exercises are given at the end of each chapter and a complete solutions manual for all exercises is available to instructors upon request. Each chapter also contains a bibliography with references covering different presentations, further applications and numerical aspects of the theory. Book jacket.

Continuum Mechanics
Continuum Mechanics

Author: I-Shih Liu

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 303

ISBN-13: 3662050560

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This concise textbook develops step by step the fundamental principles of continuum mechanics. Emphasis is on mathematical clarity, and an extended appendix provides the required background knowledge in linear algebra and tensor calculus. After introducing the basic notions about general kinematics, balance equations, material objectivity and constitutive functions, the book turns to the presentation of rational thermodynamics by stressing the role of Lagrange multipliers in deriving constitutive funcitions from the underlying entropy principle. A brief lecture on extended thermodynamics closes the book. Many examples and exercises round off the material presendted in the chapters. The book addresses primarily advanced undergraduate students in theoretical physics, applied mathematics and materials sciences.

Continuum Mechanics Through the Twentieth Century
Continuum Mechanics Through the Twentieth Century

Author: Gerard A Maugin

Publisher: Springer Science & Business Media

Published: 2013-04-08

Total Pages: 321

ISBN-13: 9400763530

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This overview of the development of continuum mechanics throughout the twentieth century is unique and ambitious. Utilizing a historical perspective, it combines an exposition on the technical progress made in the field and a marked interest in the role played by remarkable individuals and scientific schools and institutions on a rapidly evolving social background. It underlines the newly raised technical questions and their answers, and the ongoing reflections on the bases of continuum mechanics associated, or in competition, with other branches of the physical sciences, including thermodynamics. The emphasis is placed on the development of a more realistic modeling of deformable solids and the exploitation of new mathematical tools. The book presents a balanced appraisal of advances made in various parts of the world. The author contributes his technical expertise, personal recollections, and international experience to this general overview, which is very informative albeit concise.

Elements of Continuum Mechanics and Conservation Laws
Elements of Continuum Mechanics and Conservation Laws

Author: S.K. Godunov

Publisher: Springer Science & Business Media

Published: 2003-05-31

Total Pages: 270

ISBN-13: 9780306477355

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Elements of Continuum Mechanics and Conservation Laws presents a systematization of different models in mathematical physics, a study of the structure of conservation laws, thermodynamical identities, and connection with criteria for well-posedness of the corresponding mathematical problems. The theory presented in this book stems from research carried out by the authors concerning the formulations of differential equations describing explosive deformations of metals. In such processes, elasticity equations are used in some zones, whereas hydrodynamics equations are stated in other zones. Plastic deformations appear in transition zones, which leads to residual stresses. The suggested model contains some relaxation terms which simulate these plastic deformations. Certain laws of thermodynamics are used in order to describe and study differential equations simulating the physical processes. This leads to the special formulation of differential equations using generalized thermodynamical potentials.