Advances In Mathematical Modelling Of Composite Materials
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Advances in Mathematical Modelling of Composite Materials by Konstantin Z. Markov Pdf
This volume contains papers of leading experts in the modern continuum theory of composite materials. The papers expose in detail the newest ideas, approaches, results and perspectives in this broadly interdisciplinary field ranging from pure and applied mathematics, mechanics, physics and materials science. The emphasis is on mathematical modelling and model analysis of the mechanical behaviour and strength of composites, including methods of predicting effective macroscopic properties (dielectric, elastic, nonlinear, inelastic, plastic and thermoplastic) from known microstructures.
Topics in the Mathematical Modelling of Composite Materials by Andrej V. Cherkaev,Robert Kohn Pdf
Over the past several decades, we have witnessed a renaissance of theoretical work on the macroscopic behavior of microscopically heterogeneous materials. This activity brings together a number of related themes, including: (1) the use of weak convergence as a rigorous yet general language for the discussion of macroscopic behavior; (2) interest in new types of questions, particularly the "G-closure problem," motivated in large part by applications of optimal control theory to structural optimization; (3) the introduction of new methods for bounding effective moduli, including one based on "compensated compactness"; and (4) the identification of deep links between the analysis of microstructures and the multidimensional calculus of variations. This work has implications for many physical problems involving optimal design, composite materials, and coherent phase transitions. As a result, it has received attention and support from numerous scientific communities, including engineering, materials science, and physics, as well as mathematics. There is by now an extensive literature in this area. But for various reasons certain fundamental papers were never properly published, circulating instead as mimeographed notes or preprints. Other work appeared in poorly distributed conference proceedings volumes. Still other work was published in standard books or journals, but written in Russian or French. The net effect is a sort of "gap" in the literature, which has made the subject unnecessarily difficult for newcomers to penetrate. The present, softcover reprint is designed to make this classic text available to a wider audience. "Summarizes some of the fundamental results achieved and offers new perspectives in the mechanics of composite and micromechanics... Will become a classic in the two fields." —Applied Mechanics Review
Mathematical Methods And Models In Composites by Vladislav Mantic Pdf
This book provides a representative selection of the most relevant, innovative, and useful mathematical methods and models applied to the analysis and characterization of composites and their behaviour on micro-, meso-, and macroscale. It establishes the fundamentals for meaningful and accurate theoretical and computer modelling of these materials in the future. Although the book is primarily concerned with fibre-reinforced composites, which have ever-increasing applications in fields such as aerospace, many of the results presented can be applied to other kinds of composites. The topics covered include: scaling and homogenization procedures in composite structures, thin plate and wave solutions in anisotropic materials, laminated structures, instabilities, fracture and damage analysis of composites, and highly efficient methods for simulation of composites manufacturing. The results presented are useful in the design, fabrication, testing, and industrial applications of composite components and structures. The book is written by well-known experts in different areas of applied mathematics, physics, and composite engineering and is an essential source of reference for graduate and doctoral students, as well as researchers. It is also suitable for non-experts in composites who wish to have an overview of both the mathematical methods and models used in this area and the related open problems requiring further research.
Advances in Mathematical Modeling and Experimental Methods for Materials and Structures by Rivka Gilat,Leslie Banks-Sills Pdf
This collection of cutting-edge papers, written by leading authors in honor of Professor Jacob Aboudi, covers a wide spectrum of topics in the field, presents both theoretical and experimental approaches, and suggests directions for possible future research.
Finite Element Analysis of Composite Materials by Ever J. Barbero Pdf
Designing structures using composite materials poses unique challenges due especially to the need for concurrent design of both material and structure. Students are faced with two options: textbooks that teach the theory of advanced mechanics of composites, but lack computational examples of advanced analysis; and books on finite element analysis that may or may not demonstrate very limited applications to composites. But now there is third option that makes the other two obsolete: Ever J. Barbero's Finite Element Analysis of Composite Materials. By layering detailed theoretical and conceptual discussions with fully developed examples, this text supplies the missing link between theory and implementation. In-depth discussions cover all of the major aspects of advanced analysis, including three-dimensional effects, viscoelasticity, edge effects, elastic instability, damage, and delamination. More than 50 complete examples using mainly ANSYSTM, but also including some use of MATLAB®, demonstrate how to use the concepts to formulate and execute finite element analyses and how to interpret the results in engineering terms. Additionally, the source code for each example is available for download online. Cementing applied computational and analytical experience to a firm foundation of basic concepts and theory, Finite Element Analysis of Composite Materials offers a modern, practical, and versatile classroom tool for today's engineering classroom.
Mathematical Models and Methods for Smart Materials by Mauro Fabrizio,Barbara Lazzari,Angelo Morro Pdf
This book contains the papers presented at the conference on “Mathematical Models and Methods for Smart Materials”, held in Italy in 2001. The papers are divided into four parts: ”Methods in Materials Science” deals mainly with mathematical techniques for the investigation of physical systems, such as liquid crystals, materials with internal variables, amorphous materials, and thermoelastic materials. Also, techniques are exhibited for the analysis of stability and controllability of classical models of continuum mechanics and of dynamical systems. ”Modelling of Smart Materials” is devoted to models of superfluids, superconductors, materials with memory, nonlinear elastic solids, and damaged materials. In the elaboration of the models, thermodynamic aspects play a central role in the characterization of the constitutive properties. ”Well-Posedness in Materials with Memory” deals with existence, uniqueness and stability for the solution of problems, most often expressed by integrodifferential equations, which involve materials with fading memory. Also, attention is given to exponential decay in viscoelasticity, inverse problems in heat conduction with memory, and automatic control for parabolic equations. ”Analytic Problems in Phase Transitions” discusses nonlinear partial differential equations associated with phase transitions, and hysteresis, possibly involving fading memory effects. Particular applications are developed for the phase-field model with memory, the Stefan problem with a Cattaneo-type equation, the hysteresis in thermo-visco-plasticity, and the solid-solid phase transition. Contents:Automatic Control Problems for Integrodifferential Parabolic Equations (C Cavaterra)Phase Relaxation Problems with Memory and Their Optimal Control (P Colli)Unified Dynamics of Particles and Photons (G Ferrarese)Solid–Solid Phase Transition in a Mechanical System (G Gilardi)KAM Methods for Nonautonomous Schrödinger Operators (S Graffi)Fractional Diffusion and Wave Equations (A Hanyga)Recovering a Memory Kernel in an Integrodifferential Stefan Problem (L Lorenzi)Balance Equations in Two-Fluid Models of Helium II (A Morro & M Fabrizio)A Non-Stationary Model in Superconductivity (R Nibbi & M Fabrizio)Some Remarks on the Conserved Penrose-Fife Phase Field Model with Memory Effects (E Rocca)Longterm Dynamics of a Conserved Phase-Field System with Memory (F M Vegni)and other papers Readership: Researchers and academics in mathematical modeling, mathematical physics, thermodynamics, low temperature physics and classical mechanics. Keywords:Materials with Fading Memory;Thermodynamics;PDE;Phase Transitions;Smart Materials
Mathematical Models and Methods for Smart Material by Mauro Fabrizio Pdf
This book contains the papers presented at the conference on OC Mathematical Models and Methods for Smart MaterialsOCO, held in Italy in 2001. The papers are divided into four parts: OCOMethods in Materials ScienceOCO deals mainly with mathematical techniques for the investigation of physical systems, such as liquid crystals, materials with internal variables, amorphous materials, and thermoelastic materials. Also, techniques are exhibited for the analysis of stability and controllability of classical models of continuum mechanics and of dynamical systems.OCOModelling of Smart MaterialsOCO is devoted to models of superfluids, superconductors, materials with memory, nonlinear elastic solids, and damaged materials. In the elaboration of the models, thermodynamic aspects play a central role in the characterization of the constitutive properties.OCOWell-Posedness in Materials with MemoryOCO deals with existence, uniqueness and stability for the solution of problems, most often expressed by integrodifferential equations, which involve materials with fading memory. Also, attention is given to exponential decay in viscoelasticity, inverse problems in heat conduction with memory, and automatic control for parabolic equations.OCOAnalytic Problems in Phase TransitionsOCO discusses nonlinear partial differential equations associated with phase transitions, and hysteresis, possibly involving fading memory effects. Particular applications are developed for the phase-field model with memory, the Stefan problem with a Cattaneo-type equation, the hysteresis in thermo-visco-plasticity, and the solid-solid phase transition."
Moisture Transport in Polymer Composite Materials by J.M.P.Q. Delgado,A. G. Barbosa de Lima,Laura H. Carvalho Pdf
This book provides valuable information about fiber-reinforced polymer composites, with emphasis in the process of water absorption by experiments and simulation. In this monograph, we present and discuss emerging topics related to fundamentals, engineering applications, advanced mathematical modeling applied to Fickian and non-Fickian diffusion processes, analytical and computational procedures and experiments on water absorption of polymer composites reinforced by vegetable fibers. The book serves as a comprehensive learning tool for engineers, professionals, and researchers involved in this advanced interdisciplinary field, and as a reference work for both undergraduate and graduate courses.
Computational Mechanics of Composite Materials by Marcin Marek Kaminski Pdf
Computational Mechanics of Composite Materials lays stress on the advantages of combining theoretical advancements in applied mathematics and mechanics with the probabilistic approach to experimental data in meeting the practical needs of engineers. Features: Programs for the probabilistic homogenisation of composite structures with finite numbers of components allow composites to be treated as homogeneous materials with simpler behaviours. Treatment of defects in the interfaces within heterogeneous materials and those arising in composite objects as a whole by stochastic modelling. New models for the reliability of composite structures. Novel numerical algorithms for effective Monte-Carlo simulation. Computational Mechanics of Composite Materials will be of interest to academic and practising civil, mechanical, electronic and aerospatial engineers, to materials scientists and to applied mathematicians requiring accurate and usable models of the behaviour of composite materials.
Mathematical Models and Methods of Localized Interaction Theory by Abram I. Bunimovich,Anatolii V. Dubinskii Pdf
The interaction of the environment with a moving body is called ?localized? if it has been found or assumed that the force or/and thermal influence of the environment on each body surface point is independent and can be determined by the local geometrical and kinematical characteristics of this point as well as by the parameters of the environment and body?environment interactions which are the same for the whole surface of contact.Such models are widespread in aerodynamics and gas dynamics, covering supersonic and hypersonic flows, and rarefied gas flows. They describe the influence of light on a body, and are used for modelling penetration of solids into metals and soils, etc.Localized Interaction Theory (LIT) studies various theoretical and applied problems using the most general description of the influence of the environment on the body. This makes it possible to integrate results obtained from different models and to create new universal methods that can be used for various conditions, even if the description of the real interaction model is unknown. Such a unified approach to the problems of analysis, calculation and optimization of the integral characteristics of bodies moving in different media is the main content of this book which is the first monograph on this subject. Many applications, chiefly in aerodynamics and space engineering are presented.
Microscopic Theory of Condensation in Gases and Plasma by A L Itkin,E G Kolesnichenko Pdf
This book summarizes results on the creation of a new theory of condensation which has an impact on consideration of some microscopic effects left aside in the usual nucleation theories. In particular, the main idea of the authors' microscopic condensation theory is that it considers the violation of the equilibrium cluster distribution over the internal degrees of freedom due to co-occurring condensation and decay reactions of the clusters. Contents:Brief Review of the Existing Nucleation TheoriesMain Principles of the Microscopic Theory of CondensationJuxtaposition with the Other Theories and ExperimentsKinetic Theory of Photostimulated NucleationKinetic Theory of Iron-Induced NucleationConclusionsAppendices: Dimensionless Form of SystemLow-Pressure LimitQuasisteady Equations for ConcentrationsFORTRAN Subroutines for Computing Parameters of the Theory Readership: Applied mathematicians, physicists, chemists and aeronomers. keywords:Nucleation;Nonequilibrium;Kinetics;Internal Degrees of Freedom;Cluster;Ion-Induced;Photo-Stimulated;Diffusion Chamber;Analytical Solutions;New Rate Constants;Fortran Subroutines
Composite Materials Engineering by Alexander V. Vakhrushev,A. K. Haghi Pdf
This book provides a compilation of innovative fabrication strategies and utilization methodologies that are frequently adopted in the advanced composite materials community. It addresses developing appropriate composites to efficiently utilize macro- and nanoscale features. It covers a selection of key aspects of composite materials, including history, reinforcements, matrix materials, mechanical properties, physical properties, theory, and applications. The volume reviews the research developments of a number of widely studied composite materials with different matrices. Key features of this book: Contains new coverage of nanocomposites Reflects the latest theoretical and engineering and industrial applications of composite materials Provides design methods with numerical information and technical formulations needed for researchers Presents a critical review of progress in research and development on composite materials Offers comments on future research direction and ideas for product development
Advances in Composite Materials Development by Dumitra Lucan Pdf
The progress of technology is a permanent challenge in developing new materials with superior properties in terms of quality and reliability. The demand for increased performance continues to focus materials development efforts on exploring new concepts or new generations of composite materials. The chapters contained in this book represent many examples of research results dedicated to obtaining, characterizing, and mathematically modeling composite materials, especially metal matrix composites, with superior properties having a wide range of applications. The book is addressed to researchers and materials specialists, teachers and students at science and material engineering faculties, and all those interested in advances in science and technology of new materials.
Advanced Mathematical & Computational Tools in Metrology IV by P. Ciarlini Pdf
Advances in metrology depend on improvements in scientific and technical knowledge and in instrumentation quality, as well as better use of advanced mathematical tools and development of new ones. In this volume, scientists from both the mathematical and the metrological fields exchange their experiences. Industrial sectors, such as instrumentation and software, are likely to benefit from this exchange, since metrology has a high impact on the overall quality of industrial products, and applied mathematics is becoming more and more important in industrial processes.This book is of interest to people in universities, research centers and industries who are involved in measurements and need advanced mathematical tools to solve their problems, and to those developing such mathematical tools.
