Composite Media And Homogenization Theory

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Composite Media and Homogenization Theory

Author : Gianni Dal Maso
Publisher : Springer Science & Business Media
ISBN 13 : 1468467875
Total Pages : 264 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Composite Media and Homogenization Theory by : Gianni Dal Maso

Download or read book Composite Media and Homogenization Theory written by Gianni Dal Maso and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the Proceedings of the Workshop on Composite Media and Homogenization Theory held in Trieste, Italy, from January 15 to 26, 1990. The workshop was organized by the International Centre for Theo retical Physics (ICTP); part of the activity was co-sponsored by the Interna tional School for Advanced Studies (SISSA). The workshop covered a broad range of topics in the mathematical the ory of composite materials and homogenization. Among the specific areas of focus were homogenization of periodic and nonperiodic structures, porous me dia, asymptotic analysis for linear and nonlinear problems, optimal bounds for effective moduli, waves in composite materials, optimal design and relaxation, random media. The workshop was actively attended by more than 100 participants from 23 countries. In the afternoon sessions 35 seminars were delivered by the participants. This volume contains research articles corresponding to 14 of the 20 invited talks which were presented. Its content will be of interest both to mathematicians working in the field and to applied mathematicians and engineers interested in modelling the behaviour of composite and random media We are pleased to express here our thanks to the ICTP for having made this workshop possible, to Ms. A. Bergamo for her continuous help during the workshop, and to Ms. C. Parma for her collaboration in editing the proceedings. Gianni Dal Maso Gian Fausto Dell'Antonio SIS SA, Trieste Universita "La Sapienza", Roma v Contents Preface ... v List of Speakers ... ix Contributors ... ... ... ... . xiii ... ... ...

Composite Media And Homogenization Theory: Proceedings Of The Second Workshop

Author : Gianni Dal Maso
Publisher : World Scientific
ISBN 13 : 9814548529
Total Pages : 322 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Composite Media And Homogenization Theory: Proceedings Of The Second Workshop by : Gianni Dal Maso

Download or read book Composite Media And Homogenization Theory: Proceedings Of The Second Workshop written by Gianni Dal Maso and published by World Scientific. This book was released on 1995-09-30 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous mathematical treatment of the properties of composite materials has been made possible by recent mathematical results in the fields of partial differential equations and the calculus of variations. The progress in the mathematical models for composite media has led to a deeper understanding of the overall behaviour of composite structures and to significant applications in physics and engineering, including a new approach to optimal design problems.Many new, relevant results are presented in this volume, which contains 16 invited papers from the Second Workshop on Composite Media and Homogenization Theory held at the International Centre for Theoretical Physics in Trieste, Italy, from September 20 to October 1, 1993. Topics include homogenization of problems singularly depending on small or large parameters, homogenization of nonlinear problems, optimal bounds for effective moduli, asymptotic analysis of problems in perforated domains, laminate structures in phase transitions, optimal design and relaxation. Mathematicians and engineers interested in mathematical models of composite materials will find this book to be an important reference.

An Introduction to Homogenization

Author : Doïna Cioranescu
Publisher : Oxford University Press on Demand
ISBN 13 : 9780198565543
Total Pages : 262 pages
Book Rating : 4.5/5 (655 download)

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Book Synopsis An Introduction to Homogenization by : Doïna Cioranescu

Download or read book An Introduction to Homogenization written by Doïna Cioranescu and published by Oxford University Press on Demand. This book was released on 1999 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Composite materials are widely used in industry: well-known examples of this are the superconducting multi-filamentary composites which are used in the composition of optical fibres. Such materials are complicated to model, as different points in the material will have different properties. The mathematical theory of homogenization is designed to deal with this problem, and hence is used to model the behaviour of these important materials. This book provides a self-contained and authoritative introduction to the subject for graduates and researchers in the field.

Composite Media and Homogenization Theory

Author : Gianni Dal Maso
Publisher : Birkhäuser
ISBN 13 : 9780817635114
Total Pages : 0 pages
Book Rating : 4.6/5 (351 download)

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Book Synopsis Composite Media and Homogenization Theory by : Gianni Dal Maso

Download or read book Composite Media and Homogenization Theory written by Gianni Dal Maso and published by Birkhäuser. This book was released on 1991-03-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: For mathematicians and engineers interested in modeling the behavior of composite and random media, surveys recent advances using such mathematical techniques as partial differential equations and the calculus of variations. The 14 papers were originally presented at a workshop in Trieste, Italy, Ja

Homogenization Techniques for Composite Media

Author : Enrique Sanchez-Palencia
Publisher :
ISBN 13 : 9780387176161
Total Pages : 0 pages
Book Rating : 4.1/5 (761 download)

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Book Synopsis Homogenization Techniques for Composite Media by : Enrique Sanchez-Palencia

Download or read book Homogenization Techniques for Composite Media written by Enrique Sanchez-Palencia and published by . This book was released on 1987 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Composite Media and Homogenization Theory

Author : Gianni Dal Maso
Publisher : Birkhäuser
ISBN 13 : 9781468467888
Total Pages : 260 pages
Book Rating : 4.4/5 (678 download)

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Book Synopsis Composite Media and Homogenization Theory by : Gianni Dal Maso

Download or read book Composite Media and Homogenization Theory written by Gianni Dal Maso and published by Birkhäuser. This book was released on 2012-10-19 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Homogenization and Effective Moduli of Materials and Media

Author : Jerry L. Ericksen
Publisher : Springer
ISBN 13 : 9781461386483
Total Pages : 0 pages
Book Rating : 4.3/5 (864 download)

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Book Synopsis Homogenization and Effective Moduli of Materials and Media by : Jerry L. Ericksen

Download or read book Homogenization and Effective Moduli of Materials and Media written by Jerry L. Ericksen and published by Springer. This book was released on 2011-11-08 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications Homogenization and Effective Moduli of Materials and Media represents the proceedings of a workshop which was an integral part of the 19R4-R5 IMA program on CONTINUUM PHYSICS AND PARTIAL DIFFERENTIAL EQUATIONS. We are grateful to the Scientific Committee: J . L. Ericksen D. Kinderlehrer H. Brezis C. Dafermos for their dedication and hard work in rleveloping an imaginative, stimulating, and productive year-long program. George R. Sell Hans Weinherger PREFACE The papers in this volume were presented at a workshop on homogenization of differential equations and the determination of effective moduli of materials and media, primarily in the context of continuum theory. These areas are closely linked to a variety of phenomena, such as the elastic and dielectric responses of composites, and the effective properties of shales and soils. For instance, the ability to predict the effective stiffness response of a composite across a broad range of frequencies allows its performance under given circumstances to be assessed by means of nondestructive testing. A fundamental mathematical tool is homogenization, the study of partial differential equations with rapidly varying coefficients or boundary conditions. The recent alliance of homogenization with optimal design has stimulated the development of both fields. The presentations at the workshop emphasized recent advances and open questions.

Homogenization Methods for Multiscale Mechanics

Author : Chiang C. Mei
Publisher : World Scientific
ISBN 13 : 9814282448
Total Pages : 349 pages
Book Rating : 4.8/5 (142 download)

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Book Synopsis Homogenization Methods for Multiscale Mechanics by : Chiang C. Mei

Download or read book Homogenization Methods for Multiscale Mechanics written by Chiang C. Mei and published by World Scientific. This book was released on 2010 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many physical problems several scales present either in space or in time, caused by either inhomogeneity of the medium or complexity of the mechanical process. A fundamental approach is to first construct micro-scale models, and then deduce the macro-scale laws and the constitutive relations by properly averaging over the micro-scale. The perturbation method of multiple scales can be used to derive averaged equations for a much larger scale from considerations of the small scales. In the mechanics of multiscale media, the analytical scheme of upscaling is known as the Theory of Homogenization The authors share the view that the general methods of homogenization should be more widely understood and practiced by applied scientists and engineers. Hence this book is aimed at providing a less abstract treatment of the theory of homogenization for treating inhomogeneous media, and at illustrating its broad range of applications. Each chapter deals with a different class of physical problems. To tackle a new problem, the novel approach of first discussing the physically relevant scales, then identifying the small parameters and their roles in the normalized governing equations is adopted. The details of asymptotic analysis are only explained afterwards.

The Theory of Composites

Author : Graeme W. Milton
Publisher : SIAM
ISBN 13 : 1611977487
Total Pages : 761 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis The Theory of Composites by : Graeme W. Milton

Download or read book The Theory of Composites written by Graeme W. Milton and published by SIAM. This book was released on 2022-12-07 with total page 761 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Shape Optimization by the Homogenization Method

Author : Gregoire Allaire
Publisher : Springer Science & Business Media
ISBN 13 : 1468492861
Total Pages : 470 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Shape Optimization by the Homogenization Method by : Gregoire Allaire

Download or read book Shape Optimization by the Homogenization Method written by Gregoire Allaire and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the theory and numerical developments of the homogenization method. It's main features are: a comprehensive presentation of homogenization theory; an introduction to the theory of two-phase composite materials; a detailed treatment of structural optimization by using homogenization; a complete discussion of the resulting numerical algorithms with many documented test problems. It will be of interest to researchers, engineers, and advanced graduate students in applied mathematics, mechanical engineering, and structural optimization.

Multiscale Modeling Approaches for Composites

Author : George Chatzigeorgiou
Publisher : Elsevier
ISBN 13 : 0128233702
Total Pages : 366 pages
Book Rating : 4.1/5 (282 download)

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Book Synopsis Multiscale Modeling Approaches for Composites by : George Chatzigeorgiou

Download or read book Multiscale Modeling Approaches for Composites written by George Chatzigeorgiou and published by Elsevier. This book was released on 2022-01-07 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Composite Media with Weak Spatial Dispersion

Author : Constantin Simovski
Publisher : CRC Press
ISBN 13 : 1351166239
Total Pages : 296 pages
Book Rating : 4.3/5 (511 download)

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Book Synopsis Composite Media with Weak Spatial Dispersion by : Constantin Simovski

Download or read book Composite Media with Weak Spatial Dispersion written by Constantin Simovski and published by CRC Press. This book was released on 2018-11-08 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a modern theory of so-called weak spatial dispersion (WSD) in composite media of optically small inclusions without natural magnetism and optical nonlinearity. WSD manifests in two important phenomena called bianisotropy and artificial magnetism, whose microscopic origin is thoroughly studied in this book. The theory of this book is applicable to the natural media with WSD, such as chiral materials. However, emphasis is given to artificial media, too, with the idea to engineer needed electromagnetic properties. The text describes a homogenization model of effectively continuous media with multipole electromagnetic response, taking into account the interface effects. Another model is developed for so-called metamaterials in which artificial magnetism can be a resonant phenomenon and may result in the violation of Maxwell’s boundary conditions and other challenges. The book will hopefully improve the understanding of WSD and help readers to correctly describe and characterize metamaterials.

Homogenization of Differential Operators and Integral Functionals

Author : V.V. Jikov
Publisher : Springer Science & Business Media
ISBN 13 : 3642846599
Total Pages : 583 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Homogenization of Differential Operators and Integral Functionals by : V.V. Jikov

Download or read book Homogenization of Differential Operators and Integral Functionals written by V.V. Jikov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: It was mainly during the last two decades that the theory of homogenization or averaging of partial differential equations took shape as a distinct mathe matical discipline. This theory has a lot of important applications in mechanics of composite and perforated materials, filtration, disperse media, and in many other branches of physics, mechanics and modern technology. There is a vast literature on the subject. The term averaging has been usually associated with the methods of non linear mechanics and ordinary differential equations developed in the works of Poincare, Van Der Pol, Krylov, Bogoliubov, etc. For a long time, after the works of Maxwell and Rayleigh, homogeniza tion problems for· partial differential equations were being mostly considered by specialists in physics and mechanics, and were staying beyond the scope of mathematicians. A great deal of attention was given to the so called disperse media, which, in the simplest case, are two-phase media formed by the main homogeneous material containing small foreign particles (grains, inclusions). Such two-phase bodies, whose size is considerably larger than that of each sep arate inclusion, have been discovered to possess stable physical properties (such as heat transfer, electric conductivity, etc.) which differ from those of the con stituent phases. For this reason, the word homogenized, or effective, is used in relation to these characteristics. An enormous number of results, approximation formulas, and estimates have been obtained in connection with such problems as electromagnetic wave scattering on small particles, effective heat transfer in two-phase media, etc.

Composite Media with Weak Spatial Dispersion

Author : Constantin Simovski
Publisher : CRC Press
ISBN 13 : 1351166220
Total Pages : 415 pages
Book Rating : 4.3/5 (511 download)

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Book Synopsis Composite Media with Weak Spatial Dispersion by : Constantin Simovski

Download or read book Composite Media with Weak Spatial Dispersion written by Constantin Simovski and published by CRC Press. This book was released on 2018-11-08 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a modern theory of so-called weak spatial dispersion (WSD) in composite media of optically small inclusions without natural magnetism and optical nonlinearity. WSD manifests in two important phenomena called bianisotropy and artificial magnetism, whose microscopic origin is thoroughly studied in this book. The theory of this book is applicable to the natural media with WSD, such as chiral materials. However, emphasis is given to artificial media, too, with the idea to engineer needed electromagnetic properties. The text describes a homogenization model of effectively continuous media with multipole electromagnetic response, taking into account the interface effects. Another model is developed for so-called metamaterials in which artificial magnetism can be a resonant phenomenon and may result in the violation of Maxwell’s boundary conditions and other challenges. The book will hopefully improve the understanding of WSD and help readers to correctly describe and characterize metamaterials.

23rd Annual Conference on Composites, Advanced Ceramics, Materials, and Structures - B, Volume 20, Issue 4

Author : Ersan Ustundag
Publisher : John Wiley & Sons
ISBN 13 : 0470295031
Total Pages : 619 pages
Book Rating : 4.4/5 (72 download)

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Book Synopsis 23rd Annual Conference on Composites, Advanced Ceramics, Materials, and Structures - B, Volume 20, Issue 4 by : Ersan Ustundag

Download or read book 23rd Annual Conference on Composites, Advanced Ceramics, Materials, and Structures - B, Volume 20, Issue 4 written by Ersan Ustundag and published by John Wiley & Sons. This book was released on 2009-09-28 with total page 619 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is part of the Ceramic Engineering and Science Proceeding (CESP) series. This series contains a collection of papers dealing with issues in both traditional ceramics (i.e., glass, whitewares, refractories, and porcelain enamel) and advanced ceramics. Topics covered in the area of advanced ceramic include bioceramics, nanomaterials, composites, solid oxide fuel cells, mechanical properties and structural design, advanced ceramic coatings, ceramic armor, porous ceramics, and more.

Getting Acquainted with Homogenization and Multiscale

Author : Leonid Berlyand
Publisher : Springer
ISBN 13 : 303001777X
Total Pages : 178 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Getting Acquainted with Homogenization and Multiscale by : Leonid Berlyand

Download or read book Getting Acquainted with Homogenization and Multiscale written by Leonid Berlyand and published by Springer. This book was released on 2018-11-22 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of this book is to navigate beginning graduate students in mathematics and engineering through a mature field of multiscale problems in homogenization theory and to provide an idea of its broad scope. An overview of a wide spectrum of homogenization techniques ranging from classical two-scale asymptotic expansions to Gamma convergence and the rapidly developing field of stochastic homogenization is presented. The mathematical proofs and definitions are supplemented with intuitive explanations and figures to make them easier to follow. A blend of mathematics and examples from materials science and engineering is designed to teach a mixed audience of mathematical and non-mathematical students.

Mathematical Problems in Elasticity and Homogenization

Author : O.A. Oleinik
Publisher : Elsevier
ISBN 13 : 9780080875477
Total Pages : 397 pages
Book Rating : 4.8/5 (754 download)

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Book Synopsis Mathematical Problems in Elasticity and Homogenization by : O.A. Oleinik

Download or read book Mathematical Problems in Elasticity and Homogenization written by O.A. Oleinik and published by Elsevier. This book was released on 1992-11-02 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is based on research undertaken by the authors during the last ten years. The main part of the work deals with homogenization problems in elasticity as well as some mathematical problems related to composite and perforated elastic materials. This study of processes in strongly non-homogeneous media brings forth a large number of purely mathematical problems which are very important for applications. Although the methods suggested deal with stationary problems, some of them can be extended to non-stationary equations. With the exception of some well-known facts from functional analysis and the theory of partial differential equations, all results in this book are given detailed mathematical proof. It is expected that the results and methods presented in this book will promote further investigation of mathematical models for processes in composite and perforated media, heat-transfer, energy transfer by radiation, processes of diffusion and filtration in porous media, and that they will stimulate research in other problems of mathematical physics and the theory of partial differential equations.