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Multiscale Theory Of Composites And Random Media
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Book Synopsis Multiscale Theory of Composites and Random Media by : Xi Frank Xu
Download or read book Multiscale Theory of Composites and Random Media written by Xi Frank Xu and published by CRC Press. This book was released on 2018-09-21 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to introduce Green-function-based multiscale theory and the corresponding finite element method, which are readily applicable to composites and random media. The methodology is considered to be the one that most effectively tackles the uncertainty of stress propagation in complex heterogeneities of random media, and which presents multiscale theory from distinctive scale separation and scale-coupling viewpoints. Deliberately taking a multiscale perspective, it covers scale separation and then scale coupling. Both micromechanics and novel scale-coupling mechanics are described in relation to variational principles and bounds, as well as in the emerging topics on percolation and scale-coupling computation. It gives detail on the different bounds encountered, covering classical second and third order, new fourth order, and innovative ellipsoidal variations. Green-function-based multiscale theory is addressed to applications in solid mechanics and transport of complex media ranging from micro- and nano-composites, polycrystals, soils, rocks, cementitious materials, to biological materials. It is useful as a graduate textbook in civil and mechanical engineering and as a reference.
Book Synopsis Uncertainty Quantification in Multiscale Materials Modeling by : Yan Wang
Download or read book Uncertainty Quantification in Multiscale Materials Modeling written by Yan Wang and published by Woodhead Publishing. This book was released on 2020-03-12 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty Quantification in Multiscale Materials Modeling provides a complete overview of uncertainty quantification (UQ) in computational materials science. It provides practical tools and methods along with examples of their application to problems in materials modeling. UQ methods are applied to various multiscale models ranging from the nanoscale to macroscale. This book presents a thorough synthesis of the state-of-the-art in UQ methods for materials modeling, including Bayesian inference, surrogate modeling, random fields, interval analysis, and sensitivity analysis, providing insight into the unique characteristics of models framed at each scale, as well as common issues in modeling across scales.
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 2010-09-23 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many physical problems several scales are present in space or time, caused by 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 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.
Book Synopsis Multiscale Modeling and Simulation of Composite Materials and Structures by : Young Kwon
Download or read book Multiscale Modeling and Simulation of Composite Materials and Structures written by Young Kwon and published by Springer Science & Business Media. This book was released on 2007-12-04 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.
Book Synopsis Multi-Scale Continuum Mechanics Modelling of Fibre-Reinforced Polymer Composites by : Wim Van Paepegem
Download or read book Multi-Scale Continuum Mechanics Modelling of Fibre-Reinforced Polymer Composites written by Wim Van Paepegem and published by Woodhead Publishing. This book was released on 2020-11-25 with total page 766 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-scale modelling of composites is a very relevant topic in composites science. This is illustrated by the numerous sessions in the recent European and International Conferences on Composite Materials, but also by the fast developments in multi-scale modelling software tools, developed by large industrial players such as Siemens (Virtual Material Characterization toolkit and MultiMechanics virtual testing software), MSC/e-Xstream (Digimat software), Simulia (micromechanics plug-in in Abaqus), HyperSizer (Multi-scale design of composites), Altair (Altair Multiscale Designer) This book is intended to be an ideal reference on the latest advances in multi-scale modelling of fibre-reinforced polymer composites, that is accessible for both (young) researchers and end users of modelling software. We target three main groups: This book aims at a complete introduction and overview of the state-of-the-art in multi-scale modelling of composites in three axes: • ranging from prediction of homogenized elastic properties to nonlinear material behaviour • ranging from geometrical models for random packing of unidirectional fibres over meso-scale geometries for textile composites to orientation tensors for short fibre composites • ranging from damage modelling of unidirectionally reinforced composites over textile composites to short fibre-reinforced composites The book covers the three most important scales in multi-scale modelling of composites: (i) micro-scale, (ii) meso-scale and (iii) macro-scale. The nano-scale and related atomistic and molecular modelling approaches are deliberately excluded, since the book wants to focus on continuum mechanics and there are already a lot of dedicated books about polymer nanocomposites. A strong focus is put on physics-based damage modelling, in the sense that the chapters devote attention to modelling the different damage mechanisms (matrix cracking, fibre/matrix debonding, delamination, fibre fracture,...) in such a way that the underlying physics of the initiation and growth of these damage modes is respected. The book also gives room to not only discuss the finite element based approaches for multi-scale modelling, but also much faster methods that are popular in industrial software, such as Mean Field Homogenization methods (based on Mori-Tanaka and Eshelby solutions) and variational methods (shear lag theory and more advanced theories). Since the book targets a wide audience, the focus is put on the most common numerical approaches that are used in multi-scale modelling. Very specialized numerical methods like peridynamics modelling, Material Point Method, eXtended Finite Element Method (XFEM), isogeometric analysis, SPH (Smoothed Particle Hydrodynamics),... are excluded. Outline of the book The book is divided in three large parts, well balanced with each a similar number of chapters:
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.
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 187 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.
Book Synopsis Mechanics of Random and Multiscale Microstructures by : Dominique Jeulin
Download or read book Mechanics of Random and Multiscale Microstructures written by Dominique Jeulin and published by Springer. This book was released on 2014-05-04 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews recent theoretical, computational and experimental developments in mechanics of random and multiscale solid materials. The aim is to provide tools for better understanding and prediction of the effects of stochastic (non-periodic) microstructures on materials’ mesoscopic and macroscopic properties. Particular topics involve a review of experimental techniques for the microstructure description, a survey of key methods of probability theory applied to the description and representation of microstructures by random modes, static and dynamic elasticity and non-linear problems in random media via variational principles, stochastic wave propagation, Monte Carlo simulation of random continuous and discrete media, fracture statistics models, and computational micromechanics.
Book Synopsis Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures by : George Deodatis
Download or read book Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures written by George Deodatis and published by CRC Press. This book was released on 2014-02-10 with total page 1112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures contains the plenary lectures and papers presented at the 11th International Conference on STRUCTURAL SAFETY AND RELIABILITY (ICOSSAR2013, New York, NY, USA, 16-20 June 2013), and covers major aspects of safety, reliability, risk and life-cycle performance of str
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 521 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.
Book Synopsis Mechanics of Multiscale Hybrid Nanocomposites by : Farzad Ebrahimi
Download or read book Mechanics of Multiscale Hybrid Nanocomposites written by Farzad Ebrahimi and published by Elsevier. This book was released on 2022-01-25 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mechanics of Multiscale Hybrid Nanocomposites provides a practical and application-based investigation of both static and dynamic behaviors of multiscale hybrid nanocomposites. The book outlines how to predict the mechanical behavior and material characteristics of these nanocomposites via two-step micromechanical homogenization techniques performed in an energy-based approach that is incorporated with the strain-displacement relations of shear deformable beam, plate and shell theories. The effects of using various nanofillers are detailed, providing readers with the best methods of improving nanocomposite stiffness. Both numerical (Ritz, Rayleigh-Ritz, etc.) and analytical (Navier, Galerkin, etc.) solution methods are outlined, along with examples and techniques. - Demonstrates the influences of carbon nanotube agglomerates and wave phenomena on the constitutive modeling of three-phase hybrid nanocomposites - Analyzes nonlinear dynamic characteristics of hybrid nanocomposite systems, as well as how to monitor the system's stability via linearization technique - Discusses the stability of linear nanocomposite systems subjected to the dispersion of elastic waves and bending loads - Outlines how to design three-phase nanocomposite structures for resistance against buckling-mode failure - Instructs how to derive the governing equations of continuous systems in both linear and nonlinear regimes in the framework of various types of kinematic shell and plate theories
Book Synopsis Theory and Modeling of Polymer Nanocomposites by : Valeriy V. Ginzburg
Download or read book Theory and Modeling of Polymer Nanocomposites written by Valeriy V. Ginzburg and published by Springer Nature. This book was released on 2020-12-16 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume brings together the state of the art in polymer nanocomposite theory and modeling, creating a roadmap for scientists and engineers seeking to design new advanced materials. The book opens with a review of molecular and mesoscale models predicting equilibrium and non-equilibrium nanoscale structure of hybrid materials as a function of composition and, especially, filler types. Subsequent chapters cover the methods and analyses used for describing the dynamics of nanocomposites and their mechanical and physical properties. Dedicated chapters present best practices for predicting materials properties of practical interest, including thermal and electrical conductivity, optical properties, barrier properties, and flammability. Each chapter is written by leading academic and industrial scientists working in each respective sub-field. The overview of modeling methodology combined with detailed examples of property predictions for specific systems will make this book useful for academic and industrial practitioners alike.
Book Synopsis Multiscale Modeling and Uncertainty Quantification of Materials and Structures by : Manolis Papadrakakis
Download or read book Multiscale Modeling and Uncertainty Quantification of Materials and Structures written by Manolis Papadrakakis and published by Springer. This book was released on 2014-07-02 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the IUTAM Symposium on Multiscale Modeling and Uncertainty Quantification of Materials and Structures that was held at Santorini, Greece, September 9 – 11, 2013. It consists of 20 chapters which are divided in five thematic topics: Damage and fracture, homogenization, inverse problems–identification, multiscale stochastic mechanics and stochastic dynamics. Over the last few years, the intense research activity at micro scale and nano scale reflected the need to account for disparate levels of uncertainty from various sources and across scales. As even over-refined deterministic approaches are not able to account for this issue, an efficient blending of stochastic and multiscale methodologies is required to provide a rational framework for the analysis and design of materials and structures. The purpose of this IUTAM Symposium was to promote achievements in uncertainty quantification combined with multiscale modeling and to encourage research and development in this growing field with the aim of improving the safety and reliability of engineered materials and structures. Special emphasis was placed on multiscale material modeling and simulation as well as on the multiscale analysis and uncertainty quantification of fracture mechanics of heterogeneous media. The homogenization of two-phase random media was also thoroughly examined in several presentations. Various topics of multiscale stochastic mechanics, such as identification of material models, scale coupling, modeling of random microstructures, analysis of CNT-reinforced composites and stochastic finite elements, have been analyzed and discussed. A large number of papers were finally devoted to innovative methods in stochastic dynamics.
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.
Book Synopsis Multiscale Finite Element Methods by : Yalchin Efendiev
Download or read book Multiscale Finite Element Methods written by Yalchin Efendiev and published by Springer Science & Business Media. This book was released on 2009-01-10 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this monograph is to describe the main concepts and recent - vances in multiscale ?nite element methods. This monograph is intended for thebroaderaudienceincludingengineers,appliedscientists,andforthosewho are interested in multiscale simulations. The book is intended for graduate students in applied mathematics and those interested in multiscale compu- tions. It combines a practical introduction, numerical results, and analysis of multiscale ?nite element methods. Due to the page limitation, the material has been condensed. Each chapter of the book starts with an introduction and description of the proposed methods and motivating examples. Some new techniques are introduced using formal arguments that are justi?ed later in the last chapter. Numerical examples demonstrating the signi?cance of the proposed methods are presented in each chapter following the description of the methods. In the last chapter, we analyze a few representative cases with the objective of demonstrating the main error sources and the convergence of the proposed methods. A brief outline of the book is as follows. The ?rst chapter gives a general introductiontomultiscalemethodsandanoutlineofeachchapter.Thesecond chapter discusses the main idea of the multiscale ?nite element method and its extensions. This chapter also gives an overview of multiscale ?nite element methods and other related methods. The third chapter discusses the ext- sion of multiscale ?nite element methods to nonlinear problems. The fourth chapter focuses on multiscale methods that use limited global information.
Book Synopsis Wave Dispersion Characteristics of Continuous Mechanical Systems by : Farzad Ebrahimi
Download or read book Wave Dispersion Characteristics of Continuous Mechanical Systems written by Farzad Ebrahimi and published by CRC Press. This book was released on 2023-12-28 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wave Dispersion Characteristics of Continuous Mechanical Systems provides a mechanical engineering-based analysis of wave dispersion response in various structures created from different materials. Looking at materials including strengthened nanocomposites, functionally graded materials, metal foams, and anisotropic materials, it uses analytical solution methods to solve typical problems in the framework of a micromechanics approach. Nanocomposites are a novel type of composite materials, fabricated by dispersing nanosized reinforcements in a matrix to combine the material properties of the matrix with the improved properties of nanosized elements. This book enables readers to learn about the theory and practical applications of this rapidly evolving field. Practically minded, the book investigates the impact of employing various nanofillers and demonstrates how this augments stiffness within the nanocomposite. Topics covered include agglomeration and waviness of nanofillers, porosity, elastic mediums, fluid flow, and the impact of the thermal environment on a propagated wave. Using mathematical formulations to solve wave dispersion characteristics of structures including beams, plates, and shells, the book obtains equations of structures using first- and higher-order shear deformation theories. This book will be of interest to professional engineers working in material and mechanical engineering, nanocomposites, nanofillers, and micromechanics. It will also be of interest to students in these fields.
Book Synopsis Applied Mathematics Entering the 21st Century by : James M. Hill
Download or read book Applied Mathematics Entering the 21st Century written by James M. Hill and published by SIAM. This book was released on 2004-04-01 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Included in this volume are the Invited Talks given at the 5th International Congress of Industrial and Applied Mathematics. The authors of these papers are all acknowledged masters of their fields, having been chosen through a rigorous selection process by a distinguished International Program Committee. This volume presents an overview of contemporary applications of mathematics, with the coverage ranging from the rhythms of the nervous system, to optimal transportation, elasto-plasticity, computational drug design, hydrodynamic and meteorological modeling, and valuation in financial markets. Many papers are direct products of the computer revolution: grid generation, multi-scale modeling, high-dimensional numerical integration, nonlinear optimization, accurate floating-point computations and advanced iterative methods. Other papers demonstrate the close dependence on developments in mathematics itself, and the increasing importance of statistics. Additional topics relate to the study of properties of fluids and fluid-flows, or add to our understanding of Partial Differential Equations.
