Download or read book Classical Continuum Mechanics written by Karan S. Surana and published by CRC Press. This book was released on 2022-01-24 with total page 829 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Continuum Mechanics and Theory of Materials written by Peter Haupt and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Non Classical Continuum Mechanics written by Gérard A. Maugin and published by Springer. This book was released on 2016-09-24 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Continuum Mechanics written by P. Chadwick and published by Courier Corporation. This book was released on 2012-08-08 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Continuum Mechanics Modeling of Material Behavior written by Martin H. Sadd and published by Academic Press. This book was released on 2018-03-31 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Continuum Mechanics written by Fridtjov Irgens and published by Springer Science & Business Media. This book was released on 2008-01-10 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Continuum Mechanics for Engineers written by Ray M. Bowen and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Continuum Mechanics written by D. S. Chandrasekharaiah and published by Elsevier. This book was released on 2014-05-19 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed and self-contained text written for beginners, Continuum Mechanics offers concise coverage of the basic concepts, general principles, and applications of continuum mechanics. Without sacrificing rigor, the clear and simple mathematical derivations are made accessible to a large number of students with little or no previous background in solid or fluid mechanics. With the inclusion of more than 250 fully worked-out examples and 500 worked exercises, this book is certain to become a standard introductory text for students as well as an indispensable reference for professionals. Provides a clear and self-contained treatment of vectors, matrices, and tensors specifically tailored to the needs of continuum mechanics Develops the concepts and principles common to all areas in solid and fluid mechanics with a common notation and terminology Covers the fundamentals of elasticity theory and fluid mechanics
Download or read book Elements of Continuum Mechanics and Conservation Laws written by S.K. Godunov and published by Springer Science & Business Media. This book was released on 2003-05-31 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Variational Principles of Continuum Mechanics written by Victor Berdichevsky and published by Springer Science & Business Media. This book was released on 2009-09-18 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Nonlinear Continuum Mechanics and Large Inelastic Deformations written by Yuriy I. Dimitrienko and published by Springer Science & Business Media. This book was released on 2010-12-25 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a rigorous axiomatic approach to continuum mechanics under large deformation. In addition to the classical nonlinear continuum mechanics – kinematics, fundamental laws, the theory of functions having jump discontinuities across singular surfaces, etc. - the book presents the theory of co-rotational derivatives, dynamic deformation compatibility equations, and the principles of material indifference and symmetry, all in systematized form. The focus of the book is a new approach to the formulation of the constitutive equations for elastic and inelastic continua under large deformation. This new approach is based on using energetic and quasi-energetic couples of stress and deformation tensors. This approach leads to a unified treatment of large, anisotropic elastic, viscoelastic, and plastic deformations. The author analyses classical problems, including some involving nonlinear wave propagation, using different models for continua under large deformation, and shows how different models lead to different results. The analysis is accompanied by experimental data and detailed numerical results for rubber, the ground, alloys, etc. The book will be an invaluable text for graduate students and researchers in solid mechanics, mechanical engineering, applied mathematics, physics and crystallography, as also for scientists developing advanced materials.
Download or read book Continuum Mechanics Through the Twentieth Century written by Gerard A Maugin and published by Springer Science & Business Media. This book was released on 2013-04-08 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Continuum Mechanics and Thermodynamics written by Ellad B. Tadmor and published by Cambridge University Press. This book was released on 2012 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: Treats subjects directly related to nonlinear materials modeling for graduate students and researchers in physics, materials science, chemistry and engineering.
Download or read book Continuum Mechanics of Anisotropic Materials written by Stephen C. Cowin and published by Springer Science & Business Media. This book was released on 2013-01-09 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuum Mechanics of Anisotropic Materials(CMAM) presents an entirely new and unique development of material anisotropy in the context of an appropriate selection and organization of continuum mechanics topics. These features will distinguish this continuum mechanics book from other books on this subject. Textbooks on continuum mechanics are widely employed in engineering education, however, none of them deal specifically with anisotropy in materials. For the audience of Biomedical, Chemical and Civil Engineering students, these materials will be dealt with more frequently and greater accuracy in their analysis will be desired. Continuum Mechanics of Anisotropic Materials' author has been a leader in the field of developing new approaches for the understanding of anisotropic materials.
Download or read book Mathematics Applied to Continuum Mechanics written by Lee A. Segel and published by SIAM. This book was released on 2007-07-12 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Continuum Damage Mechanics written by Sumio Murakami and published by Springer Science & Business Media. This book was released on 2012-02-24 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Tensor Analysis and Continuum Mechanics written by Wilhelm Flügge and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
