Download or read book The Equations of Materials written by Brian Cantor and published by Oxford University Press. This book was released on 2020-07-24 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This primer describes important equations of materials and the scientists who derived them. It provides an excellent introduction to the subject by making the material accessible and enjoyable. The book is dedicated to a number of propositions: 1. The most important equations are often simple and easily explained; 2. The most important equations are often experimental, confirmed time and again; 3. The most important equations have been derived by remarkable scientists who lived interesting lives. Each chapter covers a single equation and materials subject, and is structured in three sections: first, a description of the equation itself; second, a short biography of the scientist after whom it is named; and third, a discussion of some of the ramifications and applications of the equation. The biographical sections intertwine the personal and professional life of the scientist with contemporary political and scientific developments. Topics included are: Bravais lattices and crystals; Bragg's law and diffraction; the Gibbs phase rule and phases; Boltzmann's equation and thermodynamics; the Arrhenius equation and reactions; the Gibbs-Thomson equation and surfaces; Fick's laws and diffusion; the Scheil equation and solidification; the Avrami equation and phase transformations; Hooke's law and elasticity; the Burgers vector and plasticity; Griffith's equation and fracture; and the Fermi level and electrical properties. The book is written for students interested in the manufacture, structure, properties and engineering application of materials such as metals, polymers, ceramics, semiconductors and composites. It requires only a working knowledge of school maths, mainly algebra and simple calculus.
Download or read book The Equations of Materials written by B. Cantor and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes some of the important equations of materials and the scientists who derived them. The text is readable and enjoyable, and is aimed at anyone interested in the manufacture, structure, properties and engineering application of materials such as metals, polymers, ceramics, semiconductors and composites.
Download or read book Constitutive Equations for Engineering Materials written by Wai-Fah Chen and published by Elsevier. This book was released on 2013-10-22 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: Constitutive Equations for Engineering Materials, Volume 1: Elasticity and Modeling, Revised Edition focuses on theories on elasticity and plasticity of engineering materials. The book first discusses vectors and tensors. Coordinate systems, vector algebra, scalar products, vector products, transformation of coordinates, indicial notation and summation convention, and triple products are then discussed. The text also ponders on analysis of stress and strain and presents numerical analysis. The book then discusses elastic stress-strain relations. Basic assumptions; need for elastic models; isotropic linear stress-strain relations; principle of virtual work; strain energy and complementary energy density in elastic solids; and incremental relations grounded on secant moduli are described. The text also explains linear elasticity and failure criteria for concrete and non-linear elasticity and hypoelastic models for concrete. The selection further tackles soil elasticity and failure criteria. Mechanical behavior of soils; failure criteria of soils; and incremental stress-strain models based on modification of the isotropic linear elastic formulation are considered. The text is a good source of data for readers interested in studying the elasticity and plasticity of engineering materials.
Download or read book The Equations World written by Boris Pritsker and published by Courier Dover Publications. This book was released on 2019-08-14 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Equations are the lifeblood of mathematics, science, and technology, and this book examines equations of all kinds. With his masterful ability to convey the excitement and elegance of mathematics, author Boris Pritsker explores equations from the simplest to the most complex—their history, their charm, and their usefulness in solving problems. The Equations World bridges the fields of algebra, geometry, number theory, and trigonometry, solving more than 280 problems by employing a wide spectrum of techniques. The author demystifies the subject with efficient hints, tricks, and methods that reveal the fun and satisfaction of problem solving. He also demonstrates how equations can serve as important tools for expressing a problem's data, showing the ways in which they assist in fitting parts together to solve the whole puzzle. In addition, brief historical tours reveal the foundations of mathematical thought by tracing the ideas and approaches developed by mathematicians over the centuries. Both recreational mathematicians and ambitious students will find this book an ample source of enlightenment and enjoyment.
Download or read book Introduction to Computational Materials Science written by Richard LeSar and published by Cambridge University Press. This book was released on 2013-03-28 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasising essential methods and universal principles, this textbook provides everything students need to understand the basics of simulating materials behaviour. All the key topics are covered from electronic structure methods to microstructural evolution, appendices provide crucial background material, and a wealth of practical resources are available online to complete the teaching package. Modelling is examined at a broad range of scales, from the atomic to the mesoscale, providing students with a solid foundation for future study and research. Detailed, accessible explanations of the fundamental equations underpinning materials modelling are presented, including a full chapter summarising essential mathematical background. Extensive appendices, including essential background on classical and quantum mechanics, electrostatics, statistical thermodynamics and linear elasticity, provide the background necessary to fully engage with the fundamentals of computational modelling. Exercises, worked examples, computer codes and discussions of practical implementations methods are all provided online giving students the hands-on experience they need.
Download or read book Constitutive Equations for Engineering Materials written by Wai-Fah Chen and published by . This book was released on 1980 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Development of the Equations of Electromagnetism in Material Continua written by Harry F. Tiersten and published by Springer Science & Business Media. This book was released on 2013-03-07 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: This tract is based on lecture notes for a course in mechanics that has been offered at Rensselaer Polytechnic Institute on and off for the past twenty years. The course is intended to provide graduate students in mechanics with an understanding of electromagnetism and prepare them for studies on the interaction of the electric and magnetic fields with deformable solid continua. As such, it is imperative that the distinction between particle and continuum descriptions of matter be carefully made and that the distinction between that which is inherently linear and that which is intrinsically nonlinear be clearly delineated. Every possible effort has been made on my part to achieve these ends. I wish to acknowledge the contributions of a number of students and faculty who attended the lectures over the years and who, by their questions and suggestions, significantly improved some of the sections. This preface would not be complete if I did not point out that my interest in electromagnetism was initiated and my attitude towards the development of the equations was influenced by lectures given by the late Professor R.D. Mindlin at Columbia University in the late nineteen fifties. I would like to thank Professor C. Truesdell for his helpful suggestions, which I feel significantly improved the clarity and readability of the Introduction, and Dr. M.G. Ancona for his comment concerning the clarity of an important point in Sec. 1.1.
Download or read book The Cahn Hilliard Equation Recent Advances and Applications written by Alain Miranville and published by SIAM. This book was released on 2019-09-09 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to present a detailed discussion of both classical and recent results on the popular Cahn–Hilliard equation and some of its variants. The focus is on mathematical analysis of Cahn–Hilliard models, with an emphasis on thermodynamically relevant logarithmic nonlinear terms, for which several questions are still open. Initially proposed in view of applications to materials science, the Cahn–Hilliard equation is now applied in many other areas, including image processing, biology, ecology, astronomy, and chemistry. In particular, the author addresses applications to image inpainting and tumor growth. Many chapters include open problems and directions for future research. The Cahn-Hilliard Equation: Recent Advances and Applications is intended for graduate students and researchers in applied mathematics, especially those interested in phase separation models and their generalizations and applications to other fields. Materials scientists also will find this text of interest.
Download or read book Dynamic Behavior of Materials written by Marc A. Meyers and published by John Wiley & Sons. This book was released on 1994-10-28 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: Addresses fundamentals and advanced topics relevant to the behavior of materials under in-service conditions such as impact, shock, stress and high-strain rate deformations. Deals extensively with materials from a microstructure perspective which is the future direction of research today.
Download or read book Constitutive Equations for Engineering Materials written by Wai-Fah Chen and published by . This book was released on 1982 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modelling of Materials Processing written by Gregory C. Stangle and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 936 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book about mathematical modelling. It focuses on the modelling of the preparation of materials. Materials are important, of course, in an economic sense: the "goods" of goods-and-services are made of materials. This provides a strong incentive to produce good materials and to improve existing materials. Mathematical modelling can help in this regard. Without a doubt, modelling a materials processing operation is not strictly necessary. Materials synthesis and fabrication processes certainly existed before the invention of mathematics and computers, and well before the combined use of mathematics and computers. Modelling can, however, be of assistance--if done properly--and if used properly. The mathematical modelling described in this book is, at its root, a rather formal, structured way of thinking about materials synthesis and fabrication processes. It requires looking at a process as a whole. It requires considering everything that is or might be important. It requires translating the details of a given physical process into one or more mathematical equations. It requires knowing how to simplify the equations without over-simplifying them.
Download or read book Statics and Mechanics of Materials written by William F. Riley and published by John Wiley & Sons. This book was released on 2001-10-30 with total page 738 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of Statics and Mechanics of Materials: An Integrated Approach continues to present students with an emphasis on the fundamental principles, with numerous applications to demonstrate and develop logical, orderly methods of procedure. Furthermore, the authors have taken measure to ensure clarity of the material for the student. Instead of deriving numerous formulas for all types of problems, the authors stress the use of free-body diagrams and the equations of equilibrium, together with the geometry of the deformed body and the observed relations between stress and strain, for the analysis of the force system action of a body.
Download or read book Transport Phenomena in Materials Processing written by David R. Poirier and published by Springer. This book was released on 2016-12-06 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides a teachable and readable approach to transport phenomena (momentum, heat, and mass transport) by providing numerous examples and applications, which are particularly important to metallurgical, ceramic, and materials engineers. Because the authors feel that it is important for students and practicing engineers to visualize the physical situations, they have attempted to lead the reader through the development and solution of the relevant differential equations by applying the familiar principles of conservation to numerous situations and by including many worked examples in each chapter. The book is organized in a manner characteristic of other texts in transport phenomena. Section I deals with the properties and mechanics of fluid motion; Section II with thermal properties and heat transfer; and Section III with diffusion and mass transfer. The authors depart from tradition by building on a presumed understanding of the relationships between the structure and properties of matter, particularly in the chapters devoted to the transport properties (viscosity, thermal conductivity, and the diffusion coefficients). In addition, generous portions of the text, numerous examples, and many problems at the ends of the chapters apply transport phenomena to materials processing.
Download or read book Strength of Materials written by Surya Patnaik and published by Butterworth-Heinemann. This book was released on 2004 with total page 774 pages. Available in PDF, EPUB and Kindle. Book excerpt: Determinate truss -- Simple beam -- Determinate shaft -- Simple frames -- Indeterminate truss -- Indeterminate beam -- Indeterminate shaft -- Indeterminate frame -- Two-dimensional structures -- Column buckling -- Energy theorems -- Finite element method -- Special topics.
Download or read book Thermodynamics of Materials with Memory written by Giovambattista Amendola and published by Springer Science & Business Media. This book was released on 2011-11-18 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a work in four parts, dealing with the mechanics and thermodynamics of materials with memory, including properties of the dynamical equations which describe their evolution in time under varying loads. The first part is an introduction to Continuum Mechanics with sections dealing with classical Fluid Mechanics and Elasticity, linear and non-linear. The second part is devoted to Continuum Thermodynamics, which is used to derive constitutive equations of materials with memory, including viscoelastic solids, fluids, heat conductors and some examples of non-simple materials. In part three, free energies for materials with linear memory constitutive relations are comprehensively explored. The new concept of a minimal state is also introduced. Formulae derived over the last decade for the minimum and related free energies are discussed in depth. Also, a new single integral free energy which is a functional of the minimal state is analyzed in detail. Finally, free energies for examples of non-simple materials are considered. In the final part, existence, uniqueness and stability results are presented for the integrodifferential equations describing the dynamical evolution of viscoelastic materials. A new approach to these topics, based on the use of minimal states rather than histories, is discussed in detail. There are also chapters on the controllability of thermoelastic systems with memory, the Saint-Venant problem for viscoelastic materials and on the theory of inverse problems.
Download or read book Materials Kinetics written by John C. Mauro and published by Elsevier. This book was released on 2020-11-22 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: Materials Kinetics: Transport and Rate Phenomena provides readers with a clear understanding of how physical-chemical principles are applied to fundamental kinetic processes. The book integrates advanced concepts with foundational knowledge and cutting-edge computational approaches, demonstrating how diffusion, morphological evolution, viscosity, relaxation and other kinetic phenomena can be applied to practical materials design problems across all classes of materials. The book starts with an overview of thermodynamics, discussing equilibrium, entropy, and irreversible processes. Subsequent chapters focus on analytical and numerical solutions of the diffusion equation, covering Fick’s laws, multicomponent diffusion, numerical solutions, atomic models, and diffusion in crystals, polymers, glasses, and polycrystalline materials. Dislocation and interfacial motion, kinetics of phase separation, viscosity, and advanced nucleation theories are examined next, followed by detailed analyses of glass transition and relaxation behavior. The book concludes with a series of chapters covering molecular dynamics, energy landscapes, broken ergodicity, chemical reaction kinetics, thermal and electrical conductivities, Monte Carlo simulation techniques, and master equations. Covers the full breadth of materials kinetics, including organic and inorganic materials, solids and liquids, theory and experiments, macroscopic and microscopic interpretations, and analytical and computational approaches Demonstrates how diffusion, viscosity microstructural evolution, relaxation, and other kinetic phenomena can be leveraged in the practical design of new materials Provides a seamless connection between thermodynamics and kinetics Includes practical exercises that reinforce key concepts at the end of each chapter
Download or read book Mechanics of Materials Formulas and Problems written by Dietmar Gross and published by Springer. This book was released on 2016-11-25 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the most important formulas and more than 140 completely solved problems from Mechanics of Materials and Hydrostatics. It provides engineering students material to improve their skills and helps to gain experience in solving engineering problems. Particular emphasis is placed on finding the solution path and formulating the basic equations. Topics include: - Stress - Strain - Hooke’s Law - Tension and Compression in Bars - Bending of Beams - Torsion - Energy Methods - Buckling of Bars - Hydrostatics
