Topics In The Mathematical Modelling Of Composite Materials
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Topics In The Mathematical Modelling Of Composite Materials
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Author : Andrej V. Cherkaev
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-08-19
Topics In The Mathematical Modelling Of Composite Materials written by Andrej V. Cherkaev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-08-19 with Mathematics categories.
Andrej V. Cherkaev and Robert V. Kohn In the past twenty years we have witnessed a renaissance of theoretical work on the macroscopic behavior of microscopically heterogeneous mate rials. 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 "com pensated 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, circu lating 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.
Topics In The Mathematical Modelling Of Composite Materials
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Author : Andrej V. Čerkaev
language : en
Publisher:
Release Date : 1997-01-01
Topics In The Mathematical Modelling Of Composite Materials written by Andrej V. Čerkaev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-01 with Composite materials categories.
Topics In The Mathematical Modelling Of Composite Materials
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Author : Andrej V. Cherkaev
language : en
Publisher: Birkhäuser
Release Date : 2011-09-27
Topics In The Mathematical Modelling Of Composite Materials written by Andrej V. Cherkaev and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-27 with Mathematics categories.
Andrej V. Cherkaev and Robert V. Kohn In the past twenty years we have witnessed a renaissance of theoretical work on the macroscopic behavior of microscopically heterogeneous mate rials. 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 "com pensated 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, circu lating 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.
Computational Mechanics Of Composite Materials
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Author : Marcin M. Kamiński
language : en
Publisher: Springer Science & Business Media
Release Date : 2005
Computational Mechanics Of Composite Materials written by Marcin M. Kamiński and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Computers categories.
This text emphasises the advantages of combining theoretical advancements in applied mathematics and mechanics with a probabilistic approach to experimental data to meet the practical needs of engineers.
The Theory Of Composites
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Author : Graeme W. Milton
language : en
Publisher: SIAM
Release Date : 2022-12-07
The Theory Of Composites written by Graeme W. Milton and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-07 with Mathematics categories.
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.
Iutam Symposium On Transformation Problems In Composite And Active Materials
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Author : Yehia A. Bahei-El-Din
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-11
Iutam Symposium On Transformation Problems In Composite And Active Materials written by Yehia A. Bahei-El-Din and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-11 with Technology & Engineering categories.
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.
Mathematical Methods And Models In Composites
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Author : Vladislav Mantic
language : en
Publisher: World Scientific
Release Date : 2013-10-25
Mathematical Methods And Models In Composites written by Vladislav Mantic and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-25 with Technology & Engineering categories.
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.
Multiscale Modeling Approaches For Composites
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Author : George Chatzigeorgiou
language : en
Publisher: Elsevier
Release Date : 2022-01-07
Multiscale Modeling Approaches For Composites written by George Chatzigeorgiou and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-07 with Technology & Engineering categories.
Multiscale Modeling Approaches for Composites outlines the fundamentals of common multiscale modeling techniques and provides detailed guidance for putting them into practice. Various homogenization methods are presented in a simple, didactic manner, with an array of numerical examples. The book starts by covering the theoretical underpinnings of tensors and continuum mechanics concepts, then passes to actual micromechanic techniques for composite media and laminate plates. In the last chapters the book covers advanced topics in homogenization, including Green's tensor, Hashin-Shtrikman bounds, and special types of problems. All chapters feature comprehensive analytical and numerical examples (Python and ABAQUS scripts) to better illustrate the theory. - Bridges theory and practice, providing step-by-step instructions for implementing multiscale modeling approaches for composites and the theoretical concepts behind them - Covers boundary conditions, data-exchange between scales, the Hill-Mandel principle, average stress and strain theorems, and more - Discusses how to obtain composite properties using different boundary conditions - Includes access to a companion site, featuring the numerical examples, Python and ABACUS codes discussed in the book
Advanced Computational Materials Modeling
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Author : Miguel Vaz Junior
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-22
Advanced Computational Materials Modeling written by Miguel Vaz Junior and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-22 with Technology & Engineering categories.
With its discussion of strategies for modeling complex materials using new numerical techniques, mainly those based on the finite element method, this monograph covers a range of topics including computational plasticity, multi-scale formulations, optimization and parameter identification, damage mechanics and nonlinear finite elements.
Mathematical Modelling Of Flow Through Porous Media Proceedings Of The Conference
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Author : Alain P Bourgeat
language : en
Publisher: World Scientific
Release Date : 1995-11-30
Mathematical Modelling Of Flow Through Porous Media Proceedings Of The Conference written by Alain P Bourgeat and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-11-30 with categories.
This proceedings volume contains contributions from leading scientists working on modelling and numerical simulation of flows through porous media and on mathematical analysis of the equations associated to the modelling. There is a number of contributions on rigorous results for stochastic media and for applications to numerical simulations. Modelling and simulation of environment and pollution are also subject of several papers. The published material herein gives an insight to the state of the art in the field with special attention for rigorous discussions and results.