Topics In The Mathematical Modelling Of Composite Materials

Author : Andrej V. Cherkaev,Robert Kohn
Publisher : Springer
Page : 317 pages
File Size : 47,8 Mb
Release : 2018-09-18
Category : Mathematics
ISBN : 9783319971841

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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

Author : Andrej V. Čerkaev
Publisher : Unknown
Page : 317 pages
File Size : 42,8 Mb
Release : 1997-01-01
Category : Composite materials
ISBN : 3764336625

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Topics in the Mathematical Modelling of Composite Materials by Andrej V. Čerkaev Pdf

Author : Konstantin Z. Markov
Publisher : World Scientific
Page : 312 pages
File Size : 41,9 Mb
Release : 1994
Category : Technology & Engineering
ISBN : 9810216440

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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.

Author : Vladislav Mantic
Publisher : World Scientific
Page : 520 pages
File Size : 40,5 Mb
Release : 2013-10-25
Category : Technology & Engineering
ISBN : 9781783264117

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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.

Author : Stefan Diebels,Sergej Rjasanow
Publisher : Springer
Page : 178 pages
File Size : 47,6 Mb
Release : 2019-02-01
Category : Science
ISBN : 9783662579572

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Multi-scale Simulation of Composite Materials by Stefan Diebels,Sergej Rjasanow Pdf

Due to their high stiffness and strength and their good processing properties short fibre reinforced thermoplastics are well-established construction materials. Up to now, simulation of engineering parts consisting of short fibre reinforced thermoplastics has often been based on macroscopic phenomenological models, but deformations, damage and failure of composite materials strongly depend on their microstructure. The typical modes of failure of short fibre thermoplastics enriched with glass fibres are matrix failure, rupture of fibres and delamination, and pure macroscopic consideration is not sufficient to predict those effects. The typical predictive phenomenological models are complex and only available for very special failures. A quantitative prediction on how failure will change depending on the content and orientation of the fibres is generally not possible, and the direct involvement of the above effects in a numerical simulation requires multi-scale modelling. One the one hand, this makes it possible to take into account the properties of the matrix material and the fibre material, the microstructure of the composite in terms of fibre content, fibre orientation and shape as well as the properties of the interface between fibres and matrix. On the other hand, the multi-scale approach links these local properties to the global behaviour and forms the basis for the dimensioning and design of engineering components. Furthermore, multi-scale numerical simulations are required to allow efficient solution of the models when investigating three-dimensional problems of dimensioning engineering parts. Bringing together mathematical modelling, materials mechanics, numerical methods and experimental engineering, this book provides a unique overview of multi-scale modelling approaches, multi-scale simulations and experimental investigations of short fibre reinforced thermoplastics. The first chapters focus on two principal subjects: the mathematical and mechanical models governing composite properties and damage description. The subsequent chapters present numerical algorithms based on the Finite Element Method and the Boundary Element Method, both of which make explicit use of the composite’s microstructure. Further, the results of the numerical simulations are shown and compared to experimental results. Lastly, the book investigates deformation and failure of composite materials experimentally, explaining the applied methods and presenting the results for different volume fractions of fibres. This book is a valuable resource for applied mathematics, theoretical and experimental mechanical engineers as well as engineers in industry dealing with modelling and simulation of short fibre reinforced composites.

Author : J.W. Bull
Publisher : Springer Science & Business Media
Page : 457 pages
File Size : 40,6 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9789401106030

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Numerical Analysis and Modelling of Composite Materials by J.W. Bull Pdf

Composite materials are increasingly used in many applications because they offer the engineer a range of advantages over traditional materials. They are often used in situations where a specified level of performance is required, but where the cost of testing the materials under the extremes of those specifications is very high. In order to solve this problem, engineers are turning to computer Modelling to evaluate the materials under the range of conditions they are likely to encounter. Many of these analyses are carried out in isolation, and yet the evaluation of a range of composites can be carried out using the same basic principles. In this new book the editor has brought together an international panel of authors, each of whom is working on the analysis and Modelling of composite materials. The overage of the book is deliberately wide; to illustrate that similar principles and methods can be used to model and evaluate a wide range of materials. It is also hoped that, by bringing together this range of topics, the insight gained in the study of one composite can be recognized and utilized in the study of others. Professional engineers involved in the specification and testing of composite material structures will find this book an invaluable resource in the course of their work. It will also be of interest to those industrial and academic engineers involved in the design, development, manufacture and applications of composite materials.

Author : Young Kwon,David H. Allen,Ramesh R. Talreja
Publisher : Springer Science & Business Media
Page : 634 pages
File Size : 40,5 Mb
Release : 2007-12-04
Category : Technology & Engineering
ISBN : 9780387363189

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Multiscale Modeling and Simulation of Composite Materials and Structures by Young Kwon,David H. Allen,Ramesh R. Talreja Pdf

This book presents the state-of-the-art in multiscale modeling and simulation techniques for composite materials and structures. It focuses on the structural and functional properties of engineering composites and the sustainable high performance of components and structures. The multiscale techniques can be also applied to nanocomposites which are important application areas in nanotechnology. There are few books available on this topic.

Author : Vladislav Mantic
Publisher : World Scientific
Page : 731 pages
File Size : 40,8 Mb
Release : 2023-03-10
Category : Mathematics
ISBN : 9781800611894

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Mathematical Methods And Models In Composites (Second Edition) by Vladislav Mantic Pdf

Mathematical Methods and Models in Composites (Second Edition) provides an in-depth treatment of modern and rigorous mathematical methods and models applied to composites modeling on the micro-, meso-, and macro scale. There has been a steady growth in the diversity of such methods and models that are used in the analysis and characterization of composites, their behavior, and their associated phenomena and processes. This second edition expands upon the success of the first edition, and has been substantially revised and updated.Written by well-known experts in different areas of applied mathematics, physics, and composite engineering, this book is mainly focused on continuous fiber reinforced composites and their ever increasing range of applications (for example, in the aerospace industry), though it also covers other kind of composites. The chapters cover a range of topics including, but not limited to: scaling and homogenization procedures in composites, thin plate and wave solutions in anisotropic materials, laminated structures, fiber-reinforced nonlinearly elastic solids, buckling and postbuckling, fracture and damage analysis of composites, and highly efficient methods for simulation of composites manufacturing such as resin transfer molding. The results presented are useful for the design, fabrication, testing and industrial applications of composite components and structures.This book is an essential reference for graduate and doctoral students, as well as researchers in mathematics, physics and composite engineering. Explanations and references in the book are sufficiently detailed so as to provide the necessary background to further investigate the fascinating subject of composites modeling and explore relevant research literature. It is also suitable for non-experts who wish to have an overview of the mathematical methods and models used for composites, and of the open problems in this area that require further research.

Author : J.M.P.Q. Delgado,A. G. Barbosa de Lima,Laura H. Carvalho
Publisher : Springer Nature
Page : 109 pages
File Size : 47,8 Mb
Release : 2022-03-19
Category : Technology & Engineering
ISBN : 9783030778262

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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.

Author : Ever J. Barbero
Publisher : CRC Press
Page : 352 pages
File Size : 40,9 Mb
Release : 2007-08-03
Category : Technology & Engineering
ISBN : 9781420054347

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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.

Author : Rivka Gilat,Leslie Banks-Sills
Publisher : Springer Science & Business Media
Page : 329 pages
File Size : 54,8 Mb
Release : 2009-12-18
Category : Science
ISBN : 9789048134670

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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.

Author : Yehia A. Bahei-El-Din,George J. Dvorak
Publisher : Springer Science & Business Media
Page : 324 pages
File Size : 49,7 Mb
Release : 2006-04-11
Category : Technology & Engineering
ISBN : 9780306469350

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IUTAM Symposium on Transformation Problems in Composite and Active Materials by Yehia A. Bahei-El-Din,George J. Dvorak Pdf

The field of composite materials has seen substantial development in the past decade, New composite systems are being continually developed for various applications. Among such systems are metal, intermetallic, and superalloy matrix composites, carbon-carbon composites as well as polymer matrix composites. At the same time, a new discipline has emerged of active or smart materials, which are often constructed as composite or heterogeneous media and structures. One unifying theme in these diverse systems is the influence that uncoupled and coupled eigenfields or transformation fields exert on the various types of overall response, as well as on the respective phase responses. Problems of this kind are currently considered by different groups which may not always appreciate the similarities of the problems involved. The purpose of the IUTAM Symposium on Transformation Problems in Composite and Active Materials held in Cairo, Egypt from March 10 to 12, 1997 was to bring together representatives of the different groups so that they may interact and explore common aspects of these seemingly different problem areas. New directions in micromechanics research in both composite and active materials were also explored in the symposium. Specifically, invited lectures in the areas of inelastic behavior of composite materials, shape memory effects, functionally graded materials, transformation problems in composite structures, and adaptive structures were delivered and discussed during the three-day meeting. This book contains the printed contributions to the IUTAM Symposium.

Author : Graeme W. Milton
Publisher : SIAM
Page : 761 pages
File Size : 45,5 Mb
Release : 2022-12-07
Category : Mathematics
ISBN : 9781611977486

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The Theory of Composites by Graeme W. Milton Pdf

Composites have been studied for more than 150 years, and interest in their properties has been growing. This classic volume provides the foundations for understanding a broad range of composite properties, including electrical, magnetic, electromagnetic, elastic and viscoelastic, piezoelectric, thermal, fluid flow through porous materials, thermoelectric, pyroelectric, magnetoelectric, and conduction in the presence of a magnetic field (Hall effect). Exact solutions of the PDEs in model geometries provide one avenue of understanding composites; other avenues include microstructure-independent exact relations satisfied by effective moduli, for which the general theory is reviewed; approximation formulae for effective moduli; and series expansions for the fields and effective moduli that are the basis of numerical methods for computing these fields and moduli. The range of properties that composites can exhibit can be explored either through the model geometries or through microstructure-independent bounds on the properties. These bounds are obtained through variational principles, analytic methods, and Hilbert space approaches. Most interesting is when the properties of the composite are unlike those of the constituent materials, and there has been an explosion of interest in such composites, now known as metamaterials. The Theory of Composites surveys these aspects, among others, and complements the new body of literature that has emerged since the book was written. It remains relevant today by providing historical background, a compendium of numerous results, and through elucidating many of the tools still used today in the analysis of composite properties. This book is intended for applied mathematicians, physicists, and electrical and mechanical engineers. It will also be of interest to graduate students.

Author : Manoochehr Zoghi
Publisher : CRC Press
Page : 708 pages
File Size : 43,5 Mb
Release : 2013-09-26
Category : Technology & Engineering
ISBN : 9780849320132

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The International Handbook of FRP Composites in Civil Engineering by Manoochehr Zoghi Pdf

Fiber-reinforced polymer (FRP) composites have become an integral part of the construction industry because of their versatility, enhanced durability and resistance to fatigue and corrosion, high strength-to-weight ratio, accelerated construction, and lower maintenance and life-cycle costs. Advanced FRP composite materials are also emerging for a wide range of civil infrastructure applications. These include everything from bridge decks, bridge strengthening and repairs, and seismic retrofit to marine waterfront structures and sustainable, energy-efficient housing. The International Handbook of FRP Composites in Civil Engineering brings together a wealth of information on advances in materials, techniques, practices, nondestructive testing, and structural health monitoring of FRP composites, specifically for civil infrastructure. With a focus on professional applications, the handbook supplies design guidelines and standards of practice from around the world. It also includes helpful design formulas, tables, and charts to provide immediate answers to common questions. Organized into seven parts, the handbook covers: FRP fundamentals, including history, codes and standards, manufacturing, materials, mechanics, and life-cycle costs Bridge deck applications and the critical topic of connection design for FRP structural members External reinforcement for rehabilitation, including the strengthening of reinforced concrete, masonry, wood, and metallic structures FRP composites for the reinforcement of concrete structures, including material characteristics, design procedures, and quality assurance–quality control (QA/QC) issues Hybrid FRP composite systems, with an emphasis on design, construction, QA/QC, and repair Quality control, quality assurance, and evaluation using nondestructive testing, and in-service monitoring using structural health monitoring of FRP composites, including smart composites that can actively sense and respond to the environment and internal states FRP-related books, journals, conference proceedings, organizations, and research sources Comprehensive yet concise, this is an invaluable reference for practicing engineers and construction professionals, as well as researchers and students. It offers ready-to-use information on how FRP composites can be more effectively utilized in new construction, repair and reconstruction, and architectural engineering.

Author : Alexander V. Vakhrushev,A. K. Haghi
Publisher : CRC Press
Page : 236 pages
File Size : 52,9 Mb
Release : 2019-10-31
Category : Science
ISBN : 9780429512490

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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