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Continuum Mechanics and Linear Elasticity

Author : Ciprian D. Coman

Publisher : Springer Nature

Page : 528 pages

File Size : 41,54 MB

Release : 2019-11-02

Category : Technology & Engineering

ISBN : 9402417710

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Book Description

This is an intermediate book for beginning postgraduate students and junior researchers, and offers up-to-date content on both continuum mechanics and elasticity. The material is self-contained and should provide readers sufficient working knowledge in both areas. Though the focus is primarily on vector and tensor calculus (the so-called coordinate-free approach), the more traditional index notation is used whenever it is deemed more sensible. With the increasing demand for continuum modeling in such diverse areas as mathematical biology and geology, it is imperative to have various approaches to continuum mechanics and elasticity. This book presents these subjects from an applied mathematics perspective. In particular, it extensively uses linear algebra and vector calculus to develop the fundamentals of both subjects in a way that requires minimal use of coordinates (so that beginning graduate students and junior researchers come to appreciate the power of the tensor notation).



Topics in Applied Continuum Mechanics

Author : J.L. Zeman

Publisher : Springer Science & Business Media

Page : 230 pages

File Size : 26,27 MB

Release : 2013-11-11

Category : Science

ISBN : 3709141885

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Book Description

THE FOUNDATIONS OF THERMOELASTICITY-EXPERIMENTS AND THEORY (A. PHILLIPS) 1. Introduction 2. The initial yield surface 4 3. The subsequent yield surface 6 4. Some theoretical consequences 10 References 13 ON THE PHYSICS AND MATHEMATICS OF SELF-STRESSES (E. KRONER) 1. Introduction 22 2. The physical origin of the self-stresses 23 3. Formulation of the mathematical problem of self-stresses 27 4. The method of modified Green's functions 30 5. Concluding remarks 35 References 38 DISTORTION IN MICROPOLAR ELASTICITY (W. NOWACKI) 1. Fundamental relations and equations 39 2. Principle of virtual work 42 3. Theorem of minimum of the complimentary work 43 • 4. Reciprocity theorem 44 5. Equations in displacements and rotations 47 6. Compatibility equations 51 References 57 THE YIELD CRITERION IN THE GENERAL CASE OF NONHOMOGENEOUS STRESS AND DEFORMATION FIELDS (J. A. KONIG and W. OLSZAK) 1. Introduction 58 2. The plasticity condition 61 3. Special cases of the yield condition 62 4. Example: Pure bending 63 5. Criteria for neutral, passive and active processes 65 VI 6. The flow law 67 References 69 ELECTRO-MAGNETO-ELASTICITY (J. B. ALBLAS) 1. Introduction 71 2. Balance equations 77 3. The jump and boundary conditions 85 4. The constitutive equations 91 5. Linearization of the magnetic problem 95 6. Magneto-elastic waves in the infinite space and in the half-space 105 References 114 PLASTICITY AND CREEP THEORY IN ENGINEERING MECHANICS (J. F • BESSE LING) 1. Introduction 115 2. Limit analysis 117 3.



Mathematics Applied to Continuum Mechanics

Author : Lee A. Segel

Publisher : SIAM

Page : 598 pages

File Size : 17,54 MB

Release : 2007-07-12

Category : Science

ISBN : 0898716209

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Book Description

This classic work gives an excellent overview of the subject, with an emphasis on clarity, explanation, and motivation. Extensive exercises and a valuable section containing hints and answers make this an excellent text for both classroom use and independent study.



A First Course in Continuum Mechanics

Author : Oscar Gonzalez

Publisher : Cambridge University Press

Page : 5 pages

File Size : 20,41 MB

Release : 2008-01-17

Category : Science

ISBN : 0521886805

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Book Description

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 for Engineers

Author : G. Thomas Mase

Publisher : CRC Press

Page : 400 pages

File Size : 38,32 MB

Release : 2009-07-28

Category : Science

ISBN : 1420085395

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Book Description

Continuum Mechanics for Engineers, Third Edition provides engineering students with a complete, concise, and accessible introduction to advanced engineering mechanics. The impetus for this latest edition was the need to suitably combine the introduction of continuum mechanics, linear and nonlinear elasticity, and viscoelasticity for a graduate-leve



Mathematical Modeling in Continuum Mechanics

Author : Roger Temam

Publisher : Cambridge University Press

Page : 356 pages

File Size : 39,4 MB

Release : 2005-05-19

Category : Science

ISBN : 1139443216

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Book Description

Temam and Miranville present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics including viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schrödinger equation. This second edition will be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level whether in engineering, mathematics, physics or the applied sciences. Exercises and hints for solutions have been added to the majority of chapters, and the final part on solid mechanics has been substantially expanded. These additions have now made it appropriate for use as a textbook, but it also remains an ideal reference book for students and anyone interested in continuum mechanics.



Classical Continuum Mechanics

Author : Karan S. Surana

Publisher : CRC Press

Page : 829 pages

File Size : 22,96 MB

Release : 2022-01-24

Category : Science

ISBN : 1000512347

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Book Description

This book provides physical and mathematical foundation as well as complete derivation of the mathematical descriptions and constitutive theories for deformation of solid and fluent continua, both compressible and incompressible with clear distinction between Lagrangian and Eulerian descriptions as well as co- and contra-variant bases. Definitions of co- and contra-variant tensors and tensor calculus are introduced using curvilinear frame and then specialized for Cartesian frame. Both Galilean and non-Galilean coordinate transformations are presented and used in establishing objective tensors and objective rates. Convected time derivatives are derived using the conventional approach as well as non-Galilean transformation and their significance is illustrated in finite deformation of solid continua as well as in the case of fluent continua. Constitutive theories are derived using entropy inequality and representation theorem. Decomposition of total deformation for solid and fluent continua into volumetric and distortional deformation is essential in providing a sound, general and rigorous framework for deriving constitutive theories. Energy methods and the principle of virtual work are demonstrated to be a small isolated subset of the calculus of variations. Differential form of the mathematical models and calculus of variations preclude energy methods and the principle of virtual work. The material in this book is developed from fundamental concepts at very basic level with gradual progression to advanced topics. This book contains core scientific knowledge associated with mathematical concepts and theories for deforming continuous matter to prepare graduate students for fundamental and basic research in engineering and sciences. The book presents detailed and consistent derivations with clarity and is ideal for self-study.



Continuum Mechanics Modeling of Material Behavior

Author : Martin H. Sadd

Publisher : Academic Press

Page : 432 pages

File Size : 47,61 MB

Release : 2018-03-31

Category : Technology & Engineering

ISBN : 0128116498

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Book Description

Continuum Mechanics Modeling of Material Behavior offers a uniquely comprehensive introduction to topics like RVE theory, fabric tensor models, micropolar elasticity, elasticity with voids, nonlocal higher gradient elasticity and damage mechanics. Contemporary continuum mechanics research has been moving into areas of complex material microstructural behavior. Graduate students who are expected to do this type of research need a fundamental background beyond classical continuum theories. The book begins with several chapters that carefully and rigorously present mathematical preliminaries: kinematics of motion and deformation; force and stress measures; and general principles of mass, momentum and energy balance. The book then moves beyond other books by dedicating several chapters to constitutive equation development, exploring a wide collection of constitutive relations and developing the corresponding material model formulations. Such material behavior models include classical linear theories of elasticity, fluid mechanics, viscoelasticity and plasticity. Linear multiple field problems of thermoelasticity, poroelasticity and electoelasticity are also presented. Discussion of nonlinear theories of solids and fluids, including finite elasticity, nonlinear/non-Newtonian viscous fluids, and nonlinear viscoelastic materials are also given. Finally, several relatively new continuum theories based on incorporation of material microstructure are presented including: fabric tensor theories, micropolar elasticity, elasticity with voids, nonlocal higher gradient elasticity and damage mechanics. - Offers a thorough, concise and organized presentation of continuum mechanics formulation - Covers numerous applications in areas of contemporary continuum mechanics modeling, including micromechanical and multi-scale problems - Integration and use of MATLAB software gives students more tools to solve, evaluate and plot problems under study - Features extensive use of exercises, providing more material for student engagement and instructor presentation



Continuum Mechanics and Theory of Materials

Author : Peter Haupt

Publisher : Springer Science & Business Media

Page : 666 pages

File Size : 27,2 MB

Release : 2013-03-14

Category : Technology & Engineering

ISBN : 3662047756

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Book Description

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

Author : Peter Chadwick

Publisher : Courier Corporation

Page : 200 pages

File Size : 36,41 MB

Release : 1999-01-01

Category : Science

ISBN : 9780486401805

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Book Description

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.