Classical Continuum Mechanics

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Classical Continuum Mechanics

Karan S. Surana
Classical Continuum Mechanics Book PDF

Author : Karan S. Surana
Publisher : CRC Press
Page : 829 pages
File Size : 50,9 Mb
Release : 2022-01-24
Category : Science
ISBN : 9781000512342

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Classical Continuum Mechanics by Karan S. Surana Pdf

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.

Non-Classical Continuum Mechanics

Gérard A. Maugin
Non Classical Continuum Mechanics Book PDF

Author : Gérard A. Maugin
Publisher : Springer
Page : 259 pages
File Size : 42,5 Mb
Release : 2016-09-24
Category : Science
ISBN : 9789811024344

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Non-Classical Continuum Mechanics by Gérard A. Maugin Pdf

This dictionary offers clear and reliable explanations of over 100 keywords covering the entire field of non-classical continuum mechanics and generalized mechanics, including the theory of elasticity, heat conduction, thermodynamic and electromagnetic continua, as well as applied mathematics. Every entry includes the historical background and the underlying theory, basic equations and typical applications. The reference list for each entry provides a link to the original articles and the most important in-depth theoretical works. Last but not least, ever y entry is followed by a cross-reference to other related subject entries in the dictionary.

Continuum Mechanics and Theory of Materials

Peter Haupt
Continuum Mechanics and Theory of Materials Book PDF

Author : Peter Haupt
Publisher : Springer Science & Business Media
Page : 666 pages
File Size : 49,5 Mb
Release : 2013-03-14
Category : Technology & Engineering
ISBN : 9783662047750

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Continuum Mechanics and Theory of Materials by Peter Haupt Pdf

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.

Variational Principles of Continuum Mechanics

Victor Berdichevsky
Variational Principles of Continuum Mechanics Book PDF

Author : Victor Berdichevsky
Publisher : Springer Science & Business Media
Page : 590 pages
File Size : 41,5 Mb
Release : 2009-09-18
Category : Science
ISBN : 9783540884675

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Variational Principles of Continuum Mechanics by Victor Berdichevsky Pdf

Thereareabout500booksonvariationalprinciples. Theyareconcernedmostlywith the mathematical aspects of the topic. The major goal of this book is to discuss the physical origin of the variational principles and the intrinsic interrelations between them. For example, the Gibbs principles appear not as the rst principles of the theory of thermodynamic equilibrium but as a consequence of the Einstein formula for thermodynamic uctuations. The mathematical issues are considered as long as they shed light on the physical outcomes and/or provide a useful technique for direct study of variational problems. Thebookisacompletelyrewrittenversionoftheauthor’smonographVariational Principles of Continuum Mechanics which appeared in Russian in 1983. I have been postponing the English translation because I wished to include the variational pr- ciples of irreversible processes in the new edition. Reaching an understanding of this subject took longer than I expected. In its nal form, this book covers all aspects of the story. The part concerned with irreversible processes is tiny, but it determines the accents put on all the results presented. The other new issues included in the book are: entropy of microstructure, variational principles of vortex line dynamics, va- ational principles and integration in functional spaces, some stochastic variational problems, variational principle for probability densities of local elds in composites with random structure, variational theory of turbulence; these topics have not been covered previously in monographic literature.

Continuum Mechanics

Fridtjov Irgens
Continuum Mechanics Book PDF

Author : Fridtjov Irgens
Publisher : Springer Science & Business Media
Page : 661 pages
File Size : 43,7 Mb
Release : 2008-01-10
Category : Science
ISBN : 9783540742982

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Continuum Mechanics by Fridtjov Irgens Pdf

This book presents an introduction into the entire science of Continuum Mechanics in three parts. The presentation is modern and comprehensive. Its introduction into tensors is very gentle. The book contains many examples and exercises, and is intended for scientists, practitioners and students of mechanics.

Continuum Mechanics Modeling of Material Behavior

Martin H. Sadd
Continuum Mechanics Modeling of Material Behavior Book PDF

Author : Martin H. Sadd
Publisher : Academic Press
Page : 432 pages
File Size : 46,8 Mb
Release : 2018-03-31
Category : Technology & Engineering
ISBN : 9780128116494

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Continuum Mechanics Modeling of Material Behavior by Martin H. Sadd Pdf

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 mass, momentum and energy balance principles. The book then moves beyond other books by dedicating the last chapter 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, as well as linear and nonlinear theories of solids and fluids, including finite elasticity, nonlinear/non-Newtonian viscous fluids, and nonlinear viscoelastic materials. 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

Elements of Continuum Mechanics and Conservation Laws

S.K. Godunov,Evgenii Romenskii
Elements of Continuum Mechanics and Conservation Laws Book PDF

Author : S.K. Godunov,Evgenii Romenskii
Publisher : Springer Science & Business Media
Page : 270 pages
File Size : 40,8 Mb
Release : 2003-05-31
Category : Computers
ISBN : 0306477351

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Elements of Continuum Mechanics and Conservation Laws by S.K. Godunov,Evgenii Romenskii Pdf

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.

Continuum Mechanics

P. Chadwick
Continuum Mechanics Book PDF

Author : P. Chadwick
Publisher : Courier Corporation
Page : 191 pages
File Size : 47,9 Mb
Release : 2012-08-08
Category : Science
ISBN : 9780486139142

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Continuum Mechanics by P. Chadwick Pdf

DIVComprehensive treatment offers 115 solved problems and exercises to promote understanding of vector and tensor theory, basic kinematics, balance laws, field equations, jump conditions, and constitutive equations. /div

Mathematics Applied to Continuum Mechanics

Lee A. Segel
Mathematics Applied to Continuum Mechanics Book PDF

Author : Lee A. Segel
Publisher : SIAM
Page : 598 pages
File Size : 43,8 Mb
Release : 2007-07-12
Category : Science
ISBN : 9780898716207

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Mathematics Applied to Continuum Mechanics by Lee A. Segel Pdf

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.

Continuum Mechanics Through the Twentieth Century

Gerard A Maugin
Continuum Mechanics Through the Twentieth Century Book PDF

Author : Gerard A Maugin
Publisher : Springer Science & Business Media
Page : 321 pages
File Size : 54,5 Mb
Release : 2013-04-08
Category : Science
ISBN : 9789400763531

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Continuum Mechanics Through the Twentieth Century by Gerard A Maugin Pdf

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.

Continuum Damage Mechanics

Sumio Murakami
Continuum Damage Mechanics Book PDF

Author : Sumio Murakami
Publisher : Springer Science & Business Media
Page : 420 pages
File Size : 48,6 Mb
Release : 2012-02-24
Category : Technology & Engineering
ISBN : 9789400726659

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Continuum Damage Mechanics by Sumio Murakami Pdf

Recent developments in engineering and technology have brought about serious and enlarged demands for reliability, safety and economy in wide range of fields such as aeronautics, nuclear engineering, civil and structural engineering, automotive and production industry. This, in turn, has caused more interest in continuum damage mechanics and its engineering applications. This book aims to give a concise overview of the current state of damage mechanics, and then to show the fascinating possibility of this promising branch of mechanics, and to provide researchers, engineers and graduate students with an intelligible and self-contained textbook. The book consists of two parts and an appendix. Part I is concerned with the foundation of continuum damage mechanics. Basic concepts of material damage and the mechanical representation of damage state of various kinds are described in Chapters 1 and 2. In Chapters 3-5, irreversible thermodynamics, thermodynamic constitutive theory and its application to the modeling of the constitutive and the evolution equations of damaged materials are descried as a systematic basis for the subsequent development throughout the book. Part II describes the application of the fundamental theories developed in Part I to typical damage and fracture problems encountered in various fields of the current engineering. Important engineering aspects of elastic-plastic or ductile damage, their damage mechanics modeling and their further refinement are first discussed in Chapter 6. Chapters 7 and 8 are concerned with the modeling of fatigue, creep, creep-fatigue and their engineering application. Damage mechanics modeling of complicated crack closure behavior in elastic-brittle and composite materials are discussed in Chapters 9 and 10. In Chapter 11, applicability of the local approach to fracture by means of damage mechanics and finite element method, and the ensuing mathematical and numerical problems are briefly discussed. A proper understanding of the subject matter requires knowledge of tensor algebra and tensor calculus. At the end of this book, therefore, the foundations of tensor analysis are presented in the Appendix, especially for readers with insufficient mathematical background, but with keen interest in this exciting field of mechanics.

Tensor Analysis and Continuum Mechanics

Wilhelm Flügge
Tensor Analysis and Continuum Mechanics Book PDF

Author : Wilhelm Flügge
Publisher : Springer Science & Business Media
Page : 215 pages
File Size : 54,9 Mb
Release : 2013-11-11
Category : Science
ISBN : 9783642883828

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Tensor Analysis and Continuum Mechanics by Wilhelm Flügge Pdf

Through several centuries there has been a lively interaction between mathematics and mechanics. On the one side, mechanics has used mathemat ics to formulate the basic laws and to apply them to a host of problems that call for the quantitative prediction of the consequences of some action. On the other side, the needs of mechanics have stimulated the development of mathematical concepts. Differential calculus grew out of the needs of Newtonian dynamics; vector algebra was developed as a means . to describe force systems; vector analysis, to study velocity fields and force fields; and the calcul~s of variations has evolved from the energy principles of mechan ics. In recent times the theory of tensors has attracted the attention of the mechanics people. Its very name indicates its origin in the theory of elasticity. For a long time little use has been made of it in this area, but in the last decade its usefulness in the mechanics of continuous media has been widely recognized. While the undergraduate textbook literature in this country was becoming "vectorized" (lagging almost half a century behind the development in Europe), books dealing with various aspects of continuum mechanics took to tensors like fish to water. Since many authors were not sure whether their readers were sufficiently familiar with tensors~ they either added' a chapter on tensors or wrote a separate book on the subject.

Cosserat Continuum Mechanics

Ioannis Vardoulakis (Deceased)
Cosserat Continuum Mechanics Book PDF

Author : Ioannis Vardoulakis (Deceased)
Publisher : Springer
Page : 179 pages
File Size : 55,9 Mb
Release : 2018-08-01
Category : Science
ISBN : 9783319951560

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Cosserat Continuum Mechanics by Ioannis Vardoulakis (Deceased) Pdf

This textbook explores the theory of Cosserat continuum mechanics, and covers fundamental tools, general laws and major models, as well as applications to the mechanics of granular media. While classical continuum mechanics is based on the axiom that the stress tensor is symmetric, theories such as that expressed in the seminal work of the brothers Eugène and François Cosserat are characterized by a non-symmetric stress tensor. The use of von Mises motor mechanics is introduced, for the compact mathematical description of the mechanics and statics of Cosserat continua, as the Cosserat continuum is a manifold of oriented “rigid particles” with 3 dofs of displacement and 3 dofs of rotation, rather than a manifold of points with 3 dofs of displacement. Here, the analysis is restricted to infinitesimal particle displacements and rotations. This book is intended as a valuable supplement to standard Continuum Mechanics courses, and graduate students as well as researchers in mechanics and applied mathematics will benefit from its self-contained text, which is enriched by numerous examples and exercises.

Introduction to Continuum Mechanics for Engineers

Ray M. Bowen
Introduction to Continuum Mechanics for Engineers Book PDF

Author : Ray M. Bowen
Publisher : Unknown
Page : 0 pages
File Size : 47,6 Mb
Release : 2009
Category : Continuum mechanics
ISBN : 0486474607

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Introduction to Continuum Mechanics for Engineers by Ray M. Bowen Pdf

This self-contained graduate-level text introduces classical continuum models within a modern framework. Its numerous exercises illustrate the governing principles, linearizations, and other approximations that constitute classical continuum models. Starting with an overview of one-dimensional continuum mechanics, the text advances to examinations of the kinematics of motion, the governing equations of balance, and the entropy inequality for a continuum. The main portion of the book involves models of material behavior and presents complete formulations of various general continuum models. The final chapter contains an introductory discussion of materials with internal state variables. Two substantial appendixes cover all of the mathematical background necessary to understand the text as well as results of representation theorems. Suitable for independent study, this volume features 280 exercises and 170 references.

An Introduction to Continuum Mechanics

Morton E. Gurtin
An Introduction to Continuum Mechanics Book PDF

Author : Morton E. Gurtin
Publisher : Academic Press
Page : 265 pages
File Size : 48,8 Mb
Release : 1982-01-12
Category : Science
ISBN : 9780080918495

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An Introduction to Continuum Mechanics by Morton E. Gurtin Pdf

This book presents an introduction to the classical theories of continuum mechanics; in particular, to the theories of ideal, compressible, and viscous fluids, and to the linear and nonlinear theories of elasticity. These theories are important, not only because they are applicable to a majority of the problems in continuum mechanics arising in practice, but because they form a solid base upon which one can readily construct more complex theories of material behavior. Further, although attention is limited to the classical theories, the treatment is modern with a major emphasis on foundations and structure