Download or read book The Mechanics and Thermodynamics of Continua written by Morton E. Gurtin and published by Cambridge University Press. This book was released on 2010-04-19 with total page 721 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mechanics and Thermodynamics of Continua presents a unified treatment of continuum mechanics and thermodynamics that emphasises the universal status of the basic balances and the entropy imbalance. These laws are viewed as fundamental building blocks on which to frame theories of material behaviour. As a valuable reference source, this book presents a detailed and complete treatment of continuum mechanics and thermodynamics for graduates and advanced undergraduates in engineering, physics and mathematics. The chapters on plasticity discuss the standard isotropic theories and, in addition, crystal plasticity and gradient plasticity.
Download or read book Mechanics of Generalized Continua written by Gérard A. Maugin and published by Springer Science & Business Media. This book was released on 2010-03-24 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: In their 1909 publication Théorie des corps déformables, Eugène and François Cosserat made a historic contribution to materials science by establishing the fundamental principles of the mechanics of generalized continua. The chapters collected in this volume showcase the many areas of continuum mechanics that grew out of the foundational work of the Cosserat brothers. The included contributions provide a detailed survey of the most recent theoretical developments in the field of generalized continuum mechanics and can serve as a useful reference for graduate students and researchers in mechanical engineering, materials science, applied physics and applied mathematics.
Download or read book Introduction to Mechanics of Continua written by William Prager and published by Courier Corporation. This book was released on 2004-01-01 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: A classic in the field, this book meets the demands of courses that establish groundwork in hydrodynamics, gas dynamics, plasticity and elasticity, and it provides typical continua problems for nonspecialists. The author addresses the major aspects of continuum studies: geometrical foundations, state of stress, instantaneous motion, fundamental laws, perfect fluids, viscous fluids, visco-plastic and perfectly plastic materials, hypoelastic materials, finite strain, and elastic and hyperelastic materials. The text’s broad converge and numerous applications include more than 160 problems and examples, and the only prerequisites are first- and second-year college calculus. 1961 ed.
Download or read book Mechanics of Continua and Wave Dynamics written by Leonid M. Brekhovskikh and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mechanics of Continua and Wave Dynamics is a textbook for a course on the mechanics of solids and fluids with the emphasis on wave theory. The material is presented with simplicity and clarity but also with mathematical rigor. Many wave phenomena, especially those of geophysical nature (different types of waves in the ocean, seismic waves in the earth crust, wave propagation in the atmosphere, etc.), are considered. Each subject is introduced with simple physical concepts using numerical examples and models. The treatment then goes into depth and complicated aspects are illustrated by appropriate generalizations. Numerous exercises with solutions will help students to comprehend and assimilate the ideas.
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 Introduction to Continuum Mechanics written by David Rubin and published by Newnes. This book was released on 2012-12-02 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuum mechanics studies the response of materials to different loading conditions. The concept of tensors is introduced through the idea of linear transformation in a self-contained chapter, and the interrelation of direct notation, indicial notation and matrix operations is clearly presented. A wide range of idealized materials are considered through simple static and dynamic problems, and the book contains an abundance of illustrative examples and problems, many with solutions. Through the addition of more advanced material (solution of classical elasticity problems, constitutive equations for viscoelastic fluids, and finite deformation theory), this popular introduction to modern continuum mechanics has been fully revised to serve a dual purpose: for introductory courses in undergraduate engineering curricula, and for beginning graduate courses.
Download or read book Theoretical Mechanics of Particles and Continua written by Alexander L. Fetter and published by Courier Corporation. This book was released on 2003-12-16 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-part text fills what has often been a void in the first-year graduate physics curriculum. Through its examination of particles and continua, it supplies a lucid and self-contained account of classical mechanics — which in turn provides a natural framework for introducing many of the advanced mathematical concepts in physics. The text opens with Newton's laws of motion and systematically develops the dynamics of classical particles, with chapters on basic principles, rotating coordinate systems, lagrangian formalism, small oscillations, dynamics of rigid bodies, and hamiltonian formalism, including a brief discussion of the transition to quantum mechanics. This part of the book also considers examples of the limiting behavior of many particles, facilitating the eventual transition to a continuous medium. The second part deals with classical continua, including chapters on string membranes, sound waves, surface waves on nonviscous fluids, heat conduction, viscous fluids, and elastic media. Each of these self-contained chapters provides the relevant physical background and develops the appropriate mathematical techniques, and problems of varying difficulty appear throughout the text.
Download or read book Continuum Mechanics with Eulerian Formulations of Constitutive Equations written by M.B. Rubin and published by Springer Nature. This book was released on 2020-10-11 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the need for an Eulerian formulation of constitutive equations. After introducing tensor analysis using both index and direct notation, nonlinear kinematics of continua is presented. The balance laws of the purely mechanical theory are discussed along with restrictions on constitutive equations due to superposed rigid body motion. The balance laws of the thermomechanical theory are discussed and specific constitutive equations are presented for: hyperelastic materials; elastic–inelastic materials; thermoelastic–inelastic materials with application to shock waves; thermoelastic–inelastic porous materials; and thermoelastic–inelastic growing biological tissues.
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 Hamilton s Principle in Continuum Mechanics written by Anthony Bedford and published by Springer Nature. This book was released on 2021-12-14 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised, updated edition provides a comprehensive and rigorous description of the application of Hamilton’s principle to continuous media. To introduce terminology and initial concepts, it begins with what is called the first problem of the calculus of variations. For both historical and pedagogical reasons, it first discusses the application of the principle to systems of particles, including conservative and non-conservative systems and systems with constraints. The foundations of mechanics of continua are introduced in the context of inner product spaces. With this basis, the application of Hamilton’s principle to the classical theories of fluid and solid mechanics are covered. Then recent developments are described, including materials with microstructure, mixtures, and continua with singular surfaces.
Download or read book Continuum Mechanics written by Antonio Romano and published by Springer Science & Business Media. This book was released on 2010-07-23 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a broad overview of the potential of continuum mechanics to describe a wide range of macroscopic phenomena in real-world problems. Building on the fundamentals presented in the authors’ previous book, Continuum Mechanics using Mathematica®, this new work explores interesting models of continuum mechanics, with an emphasis on exploring the flexibility of their applications in a wide variety of fields.
Download or read book Fundamentals of Continuum Mechanics written by John W. Rudnicki and published by John Wiley & Sons. This book was released on 2014-09-22 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise introductory course text on continuum mechanics Fundamentals of Continuum Mechanics focuses on the fundamentals of the subject and provides the background for formulation of numerical methods for large deformations and a wide range of material behaviours. It aims to provide the foundations for further study, not just of these subjects, but also the formulations for much more complex material behaviour and their implementation computationally. This book is divided into 5 parts, covering mathematical preliminaries, stress, motion and deformation, balance of mass, momentum and energy, and ideal constitutive relations and is a suitable textbook for introductory graduate courses for students in mechanical and civil engineering, as well as those studying material science, geology and geophysics and biomechanics. A concise introductory course text on continuum mechanics Covers the fundamentals of continuum mechanics Uses modern tensor notation Contains problems and accompanied by a companion website hosting solutions Suitable as a textbook for introductory graduate courses for students in mechanical and civil engineering
Download or read book Advanced Methods of Continuum Mechanics for Materials and Structures written by Konstantin Naumenko and published by Springer. This book was released on 2016-05-12 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a collection of contributions on advanced approaches of continuum mechanics, which were written to celebrate the 60th birthday of Prof. Holm Altenbach. The contributions are on topics related to the theoretical foundations for the analysis of rods, shells and three-dimensional solids, formulation of constitutive models for advanced materials, as well as development of new approaches to the modeling of damage and fractures.
Download or read book Cosserat Continuum Mechanics written by Ioannis Vardoulakis (Deceased) and published by Springer. This book was released on 2018-08-01 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 Physical Foundations of Continuum Mechanics written by A. Ian Murdoch and published by Cambridge University Press. This book was released on 2012-10-22 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ian Murdoch's Physical Foundations of Continuum Mechanics will interest engineers, mathematicians, and physicists who study the macroscopic behaviour of solids and fluids or engage in molecular dynamical simulations. In contrast to standard works on the subject, Murdoch's book examines physical assumptions implicit in continuum modelling from a molecular perspective. In so doing, physical interpretations of concepts and fields are clarified by emphasising both their microscopic origin and sensitivity to scales of length and time. Murdoch expertly applies this approach to theories of mixtures, generalised continua, fluid flow through porous media, and systems whose molecular content changes with time. Elements of statistical mechanics are included, for comparison, and two extensive appendices address relevant mathematical concepts and results. This unique and thorough work is an authoritative reference for both students and experts in the field.
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.
