Topics in the Mathematical Modelling of Composite Materials

Topics in the Mathematical Modelling of Composite Materials

Author: Andrej V. Cherkaev

Publisher: Springer

Published: 2018-09-18

Total Pages: 317

ISBN-13: 3319971840

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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


Book Synopsis Topics in the Mathematical Modelling of Composite Materials by : Andrej V. Cherkaev

Download or read book Topics in the Mathematical Modelling of Composite Materials written by Andrej V. Cherkaev and published by Springer. This book was released on 2018-09-18 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Topics in the Mathematical Modelling of Composite Materials

Topics in the Mathematical Modelling of Composite Materials

Author: Andrej V. Čerkaev

Publisher:

Published: 1997-01-01

Total Pages: 317

ISBN-13: 9783764336622

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Book Synopsis Topics in the Mathematical Modelling of Composite Materials by : Andrej V. Čerkaev

Download or read book Topics in the Mathematical Modelling of Composite Materials written by Andrej V. Čerkaev and published by . This book was released on 1997-01-01 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Advances in Mathematical Modelling of Composite Materials

Advances in Mathematical Modelling of Composite Materials

Author: Konstantin Z. Markov

Publisher: World Scientific

Published: 1994

Total Pages: 312

ISBN-13: 9789810216443

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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.


Book Synopsis Advances in Mathematical Modelling of Composite Materials by : Konstantin Z. Markov

Download or read book Advances in Mathematical Modelling of Composite Materials written by Konstantin Z. Markov and published by World Scientific. This book was released on 1994 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Methods And Models In Composites

Mathematical Methods And Models In Composites

Author: Vladislav Mantic

Publisher: World Scientific

Published: 2013-10-25

Total Pages: 520

ISBN-13: 178326411X

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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.


Book Synopsis Mathematical Methods And Models In Composites by : Vladislav Mantic

Download or read book Mathematical Methods And Models In Composites written by Vladislav Mantic and published by World Scientific. This book was released on 2013-10-25 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Multi-scale Simulation of Composite Materials

Multi-scale Simulation of Composite Materials

Author: Stefan Diebels

Publisher: Springer

Published: 2019-02-01

Total Pages: 178

ISBN-13: 366257957X

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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.


Book Synopsis Multi-scale Simulation of Composite Materials by : Stefan Diebels

Download or read book Multi-scale Simulation of Composite Materials written by Stefan Diebels and published by Springer. This book was released on 2019-02-01 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Methods And Models In Composites (Second Edition)

Mathematical Methods And Models In Composites (Second Edition)

Author: Vladislav Mantic

Publisher: World Scientific

Published: 2023-03-10

Total Pages: 731

ISBN-13: 1800611897

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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.


Book Synopsis Mathematical Methods And Models In Composites (Second Edition) by : Vladislav Mantic

Download or read book Mathematical Methods And Models In Composites (Second Edition) written by Vladislav Mantic and published by World Scientific. This book was released on 2023-03-10 with total page 731 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Numerical Analysis and Modelling of Composite Materials

Numerical Analysis and Modelling of Composite Materials

Author: J.W. Bull

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 457

ISBN-13: 9401106037

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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.


Book Synopsis Numerical Analysis and Modelling of Composite Materials by : J.W. Bull

Download or read book Numerical Analysis and Modelling of Composite Materials written by J.W. Bull and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Moisture Transport in Polymer Composite Materials

Moisture Transport in Polymer Composite Materials

Author: J.M.P.Q. Delgado

Publisher: Springer Nature

Published: 2022-03-19

Total Pages: 109

ISBN-13: 3030778266

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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.


Book Synopsis Moisture Transport in Polymer Composite Materials by : J.M.P.Q. Delgado

Download or read book Moisture Transport in Polymer Composite Materials written by J.M.P.Q. Delgado and published by Springer Nature. This book was released on 2022-03-19 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Multiscale Modeling and Simulation of Composite Materials and Structures

Multiscale Modeling and Simulation of Composite Materials and Structures

Author: Young W. Kwon

Publisher: Springer Science & Business Media

Published: 2007-10-23

Total Pages: 634

ISBN-13: 0387685561

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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.


Book Synopsis Multiscale Modeling and Simulation of Composite Materials and Structures by : Young W. Kwon

Download or read book Multiscale Modeling and Simulation of Composite Materials and Structures written by Young W. Kwon and published by Springer Science & Business Media. This book was released on 2007-10-23 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Computational Mechanics of Composite Materials

Computational Mechanics of Composite Materials

Author: Marcin Marek Kaminski

Publisher: Springer Science & Business Media

Published: 2006-03-30

Total Pages: 434

ISBN-13: 1846280494

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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.


Book Synopsis Computational Mechanics of Composite Materials by : Marcin Marek Kaminski

Download or read book Computational Mechanics of Composite Materials written by Marcin Marek Kaminski and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.