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: 327

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

Topics in the Mathematical Modelling of Composite Materials
Topics in the Mathematical Modelling of Composite Materials

Author: Andrej V. Cherkaev

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 329

ISBN-13: 1461220327

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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.

The Theory of Composites
The Theory of Composites

Author: Graeme W. Milton

Publisher: SIAM

Published: 2022-12-07

Total Pages: 761

ISBN-13: 1611977487

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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
Shape Optimization by the Homogenization Method

Author: Gregoire Allaire

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 470

ISBN-13: 1468492861

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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.

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.

Damage Modeling of Composite Structures
Damage Modeling of Composite Structures

Author: Pengfei Liu

Publisher: Elsevier

Published: 2021-03-09

Total Pages: 396

ISBN-13: 0128209631

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Damage Modeling of Composite Structures: Strength, Fracture, and Finite Element Analysis provides readers with a fundamental overview of the mechanics of composite materials, along with an outline of an array of modeling and numerical techniques used to analyze damage, failure mechanisms and safety tolerance. Strength prediction and finite element analysis of laminated composite structures are both covered, as are modeling techniques for delaminated composites under compression and shear. Viscoelastic cohesive/friction coupled model and finite element analysis for delamination analysis of composites under shear and for laminates under low-velocity impact are all covered at length. A concluding chapter discusses multiscale damage models and finite element analysis of composite structures. Integrates intralaminar damage and interlaminar delamination under different load patterns, covering intralaminar damage constitutive models, failure criteria, damage evolution laws, and virtual crack closure techniques Discusses numerical techniques for progressive failure analysis and modeling, as well as numerical convergence and mesh sensitivity, thus allowing for more accurate modeling Features models and methods that can be seamlessly extended to analyze failure mechanisms and safety tolerance of composites under more complex loads, and in more extreme environments Demonstrates applications of damage models and numerical methods

Residual Stresses in Composite Materials
Residual Stresses in Composite Materials

Author: Mahmood M. Shokrieh

Publisher: Woodhead Publishing

Published: 2014-02-14

Total Pages: 407

ISBN-13: 0857098594

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Residual stresses are a common phenomenon in composite materials. They can either add to or significantly reduce material strength. Because of the increasing demand for high-strength, light-weight materials such as composites and their wide range of applications in the aerospace and automotive industries, in civil infrastructure and in sporting applications, it is critical that the residual stresses of composite materials are understood and measured correctly.The first part of this important book reviews destructive and non-destructive testing (NDT) techniques for measuring residual stresses. Various mathematical (analytical and numerical) methods for calculation of residual stresses in composite materials are also presented. Chapters in the first section of the book discuss the simulated hole drilling method, the slitting/crack compliance method, measuring residual stresses in homogeneous and composite glass materials using photoelastic techniques, and modeling residual stresses in composite materials. The second part of the book discusses residual stresses in polymer matrix, metal-matrix and a range of other types of composites. Moreover, the addition of nanoparticles to the matrix of polymeric composites as a new technique for reduction of residual stresses is discussed.Residual stresses in composite materials provides a comprehensive overview of this important topic, and is an invaluable reference text for both academics and professionals working in the mechanical engineering, civil engineering, aerospace, automotive, marine and sporting industries. - Reviews destructive and non-destructive testing (NDT) techniques for measuring residual stresses - Discusses residual stresses in polymer matrix, metal-matrix and other types of composite - Considers the addition of nanoparticles to the matrix of polymeric composites as a new technique for reduction of residual stresses

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.

Multi-scale Modelling for Structures and Composites
Multi-scale Modelling for Structures and Composites

Author: G. Panasenko

Publisher: Springer Science & Business Media

Published: 2005-02-09

Total Pages: 426

ISBN-13: 9781402029813

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Numerous applications of rod structures in civil engineering, aircraft and spacecraft confirm the importance of the topic. On the other hand the majority of books on structural mechanics use some simplifying hypotheses; these hypotheses do not allow to consider some important effects, for instance the boundary layer effects near the points of junction of rods. So the question concerning the limits of applicability of structural mechanics hypotheses and the possibilities of their refinement arise. In this connection the asymptotic analysis of equations of mathematical physics, the equations of elasticity in rod structures (without these hypotheses and simplifying assumptions being imposed) is undertaken in the present book. Moreover, a lot of modern structures are made of composite materials and therefore the material of the rods is not homogeneous. This inhomogeneity of the material can generate some unexpected effects. These effects are analysed in this book. The methods of multi-scale modelling are presented by the homogenization, multi-level asymptotic analysis and the domain decomposition. These methods give an access to a new class of hybrid models combining macroscopic description with "microscopic zooms".

Electrothermics
Electrothermics

Author: Javad Fouladgar

Publisher: John Wiley & Sons

Published: 2012-12-13

Total Pages: 255

ISBN-13: 1118563085

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This book concerns the analysis and design of induction heating of poor electrical conduction materials. Some innovating applications such as inductive plasma installation or transformers, thermo inductive non-destructive testing and carbon-reinforced composite materials heating are studied. Analytical, semi-analytical and numerical models are combined to obtain the best modeling technique for each case. Each model has been tested with experimental results and validated. The principal aspects of a computational package to solve these kinds of coupled problems are described. In the first chapter, the mathematical tools for coupled electromagnetic and thermal phenomena are introduced. In Chapter 2, these tools are used to analyze a radio frequency inductive plasma installation. The third chapter describes the methodology of designing a low frequency plasma transformer. Chapter 4 studies the feasibility of the thermo inductive technique for non-destructive testing and the final chapter is dedicated to the use of induction heating in the lifecycle of carbon-reinforced composite materials. Contents 1. Thermal and Electromagnetic Coupling, Javad Fouladgar, Didier Trichet and Brahim Ramdane. 2. Simplified Model of a Radiofrequency Inductive Thermal Plasma Installation, Javad Fouladgar and Jean-Pierre Ploteau. 3. Design Methodology of A Very Low-Frequency Plasma Transformer, Javad Fouladgar and Souri Mohamed Mimoune. 4. Non Destructive Testing by Thermo-Inductive Method, Javad Fouladgar, Brahim Ramdane, Didier Trichet and Tayeb Saidi. 5. Induction Heating of Composite Materials, Javad Fouladgar, Didier Trichet, Samir Bensaid and Guillaume Wasselynck