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Homogenization Methods
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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 2010-09-23 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 Homogenization by : Gregori A. Chechkin
Download or read book Homogenization written by Gregori A. Chechkin and published by American Mathematical Soc.. This book was released on with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on both classical results of homogenization theory and modern techniques developed over the past decade. The powerful techniques in partial differential equations are illustrated with many exercises and examples to enhance understanding of the material. Several of the modern topics that are presented have not previously appeared in any monograph.
Book Synopsis Homogenization Methods by : Rainer Glüge
Download or read book Homogenization Methods written by Rainer Glüge and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-02-20 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Almost all materials posses a microstructure, which cannot be accounted for in detail in structural engineering calculations. Instead, effective material properties are used. These are obtained by homogenization methods. This book provides
Book Synopsis Multiscale Methods by : Grigoris Pavliotis
Download or read book Multiscale Methods written by Grigoris Pavliotis and published by Springer Science & Business Media. This book was released on 2008-01-18 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to multiscale methods gives you a broad overview of the methods’ many uses and applications. The book begins by setting the theoretical foundations of the methods and then moves on to develop models and prove theorems. Extensive use of examples shows how to apply multiscale methods to solving a variety of problems. Exercises then enable you to build your own skills and put them into practice. Extensions and generalizations of the results presented in the book, as well as references to the literature, are provided in the Discussion and Bibliography section at the end of each chapter.With the exception of Chapter One, all chapters are supplemented with exercises.
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.
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.
Book Synopsis Computational Homogenization of Heterogeneous Materials with Finite Elements by : Julien Yvonnet
Download or read book Computational Homogenization of Heterogeneous Materials with Finite Elements written by Julien Yvonnet and published by Springer. This book was released on 2019-06-11 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a concise overview of the main theoretical and numerical tools to solve homogenization problems in solids with finite elements. Starting from simple cases (linear thermal case) the problems are progressively complexified to finish with nonlinear problems. The book is not an overview of current research in that field, but a course book, and summarizes established knowledge in this area such that students or researchers who would like to start working on this subject will acquire the basics without any preliminary knowledge about homogenization. More specifically, the book is written with the objective of practical implementation of the methodologies in simple programs such as Matlab. The presentation is kept at a level where no deep mathematics are required.
Book Synopsis From Creep Damage Mechanics to Homogenization Methods by : Holm Altenbach
Download or read book From Creep Damage Mechanics to Homogenization Methods written by Holm Altenbach and published by Springer. This book was released on 2015-06-03 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a collection of contributions on materials modeling, which were written to celebrate the 65th birthday of Prof. Nobutada Ohno. The book follows Prof. Ohno’s scientific topics, starting with creep damage problems and ending with homogenization methods.
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.
Book Synopsis Homogenization of Reticulated Structures by : Doina Cioranescu
Download or read book Homogenization of Reticulated Structures written by Doina Cioranescu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: Materials science is an area of growing research as composite materials become widely used in such areas as civil engineering, electrotechnics, and the aerospace industry. This mathematically rigorous treatment of lattice-type structures will appeal to both applied mathematicians, as well as engineers looking for a solid mathematical foundation of the methodology.
Book Synopsis Homogenization and Structural Topology Optimization by : Behrooz Hassani
Download or read book Homogenization and Structural Topology Optimization written by Behrooz Hassani and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Structural topology optimization is a fast growing field that is finding numerous applications in automotive, aerospace and mechanical design processes. Homogenization is a mathematical theory with applications in several engineering problems that are governed by partial differential equations with rapidly oscillating coefficients Homogenization and Structural Topology Optimization brings the two concepts together and successfully bridges the previously overlooked gap between the mathematical theory and the practical implementation of the homogenization method. The book is presented in a unique self-teaching style that includes numerous illustrative examples, figures and detailed explanations of concepts. The text is divided into three parts which maintains the book's reader-friendly appeal.
Book Synopsis Homogenization Methods in Partial Differential Equations and Modeling Multiphase Materials by : Chaocheng Huang
Download or read book Homogenization Methods in Partial Differential Equations and Modeling Multiphase Materials written by Chaocheng Huang and published by . This book was released on 1995 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Homogenization by : Gregori A. Chechkin
Download or read book Homogenization written by Gregori A. Chechkin and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Homogenization is a collection of powerful techniques in partial differential equations that are used to study differential operators with rapidly oscillating coefficients, boundary value problems with rapidly varying boundary conditions, equations in perforated domains, equations with random coefficients, and other objects of theoretical and practical interest. The book focuses on various aspects of homogenization theory and related topics. It comprises classical results and methods of homogenization theory, as well as modern subjects and techniques developed in the last decade. Special atten.
Book Synopsis Homogenization of Coupled Phenomena in Heterogenous Media by : Jean-Louis Auriault
Download or read book Homogenization of Coupled Phenomena in Heterogenous Media written by Jean-Louis Auriault and published by John Wiley & Sons. This book was released on 2010-01-05 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: Both naturally-occurring and man-made materials are often heterogeneous materials formed of various constituents with different properties and behaviours. Studies are usually carried out on volumes of materials that contain a large number of heterogeneities. Describing these media by using appropriate mathematical models to describe each constituent turns out to be an intractable problem. Instead they are generally investigated by using an equivalent macroscopic description - relative to the microscopic heterogeneity scale - which describes the overall behaviour of the media. Fundamental questions then arise: Is such an equivalent macroscopic description possible? What is the domain of validity of this macroscopic description? The homogenization technique provides complete and rigorous answers to these questions. This book aims to summarize the homogenization technique and its contribution to engineering sciences. Researchers, graduate students and engineers will find here a unified and concise presentation. The book is divided into four parts whose main topics are Introduction to the homogenization technique for periodic or random media, with emphasis on the physics involved in the mathematical process and the applications to real materials. Heat and mass transfers in porous media Newtonian fluid flow in rigid porous media under different regimes Quasi-statics and dynamics of saturated deformable porous media Each part is illustrated by numerical or analytical applications as well as comparison with the self-consistent approach.
Book Synopsis Microstructural Modeling and Computational Homogenization of the Physically Linear and Nonlinear Constitutive Behavior of Micro-heterogeneous Materials by : Felix Fritzen
Download or read book Microstructural Modeling and Computational Homogenization of the Physically Linear and Nonlinear Constitutive Behavior of Micro-heterogeneous Materials written by Felix Fritzen and published by KIT Scientific Publishing. This book was released on 2014-08-22 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineering materials show a pronounced heterogeneity on a smaller scale that influences the macroscopic constitutive behavior. Algorithms for the periodic discretization of microstructures are presented. These are used within the Nonuniform Transformation Field Analysis (NTFA) which is an order reduction based nonlinear homogenization method with micro-mechanical background. Theoretical and numerical aspects of the method are discussed and its computational efficiency is validated.
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 Instrumental Methods in Metal Ion Speciation by : Imran Ali
Download or read book Instrumental Methods in Metal Ion Speciation written by Imran Ali and published by CRC Press. This book was released on 2006-03-14 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The knowledge of metal ion speciation is essential for predicting the exact toxicities of metal ion species in the environment. Metal ions can exist in various oxidation states, each of which possesses different physical and chemical properties as well as exhibit varying toxicities. Often, toxicity data is unreliable because it is based on metal io
