Homogenization and Applications to Material Sciences PDF Download

Author: Doina Cioranescu
Publisher:
ISBN:
Category : Composite materials
Languages : en
Pages : 456

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Author: P. Ponte Castaneda
Publisher: Springer Science & Business Media
ISBN: 1402026234
Category : Technology & Engineering
Languages : en
Pages : 371

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Book Description
Although several books and conference proceedings have already appeared dealing with either the mathematical aspects or applications of homogenization theory, there seems to be no comprehensive volume dealing with both aspects. The present volume is meant to fill this gap, at least partially, and deals with recent developments in nonlinear homogenization emphasizing applications of current interest. It contains thirteen key lectures presented at the NATO Advanced Workshop on Nonlinear Homogenization and Its Applications to Composites, Polycrystals and Smart Materials. The list of thirty one contributed papers is also appended. The key lectures cover both fundamental, mathematical aspects of homogenization, including nonconvex and stochastic problems, as well as several applications in micromechanics, thin films, smart materials, and structural and topology optimization. One lecture deals with a topic important for nanomaterials: the passage from discrete to continuum problems by using nonlinear homogenization methods. Some papers reveal the role of parameterized or Young measures in description of microstructures and in optimal design. Other papers deal with recently developed methods – both analytical and computational – for estimating the effective behavior and field fluctuations in composites and polycrystals with nonlinear constitutive behavior. All in all, the volume offers a cross-section of current activity in nonlinear homogenization including a broad range of physical and engineering applications. The careful reader will be able to identify challenging open problems in this still evolving field. For instance, there is the need to improve bounding techniques for nonconvex problems, as well as for solving geometrically nonlinear optimum shape-design problems, using relaxation and homogenization methods.

Author: N.S. Bakhvalov
Publisher: Springer Science & Business Media
ISBN: 9400922477
Category : Mathematics
Languages : en
Pages : 400

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Book Description
'Et moi, .... si j'avait su comment en revenir, One service mathematics has rendered the je n'y semis point all,,: human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent: therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non !inearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Author: Andrea Braides
Publisher: Springer Science & Business Media
ISBN: 354036546X
Category : Mathematics
Languages : en
Pages : 326

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The study of variational problems showing multi-scale behaviour with oscillation or concentration phenomena is a challenging topic of very active research. This volume collects lecture notes on the asymptotic analysis of such problems when multi-scale behaviour derives from scale separation in the passage from atomistic systems to continuous functionals, from competition between bulk and surface energies, from various types of homogenization processes, and on concentration effects in Ginzburg-Landau energies and in subcritical growth problems.

Author: Gui-Qiang G. Chen
Publisher: Springer
ISBN: 331918573X
Category : Mathematics
Languages : en
Pages : 384

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Book Description
This book examines the exciting interface between differential geometry and continuum mechanics, now recognised as being of increasing technological significance. Topics discussed include isometric embeddings in differential geometry and the relation with microstructure in nonlinear elasticity, the use of manifolds in the description of microstructure in continuum mechanics, experimental measurement of microstructure, defects, dislocations, surface energies, and nematic liquid crystals. Compensated compactness in partial differential equations is also treated. The volume is intended for specialists and non-specialists in pure and applied geometry, continuum mechanics, theoretical physics, materials and engineering sciences, and partial differential equations. It will also be of interest to postdoctoral scientists and advanced postgraduate research students. These proceedings include revised written versions of the majority of papers presented by leading experts at the ICMS Edinburgh Workshop on Differential Geometry and Continuum Mechanics held in June 2013. All papers have been peer reviewed.

Author: Subhendu Ray Chowdhury
Publisher: CRC Press
ISBN: 1000807231
Category : Technology & Engineering
Languages : en
Pages : 417

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This book explains various kinds of non-ionizing and high-energy radiations, their interaction with materials and chemical reactions, and conditions of various kinds of materials development technologies including applications. It covers a processing-structure-property relationship and radiations used in developing many advanced materials used in various fields. It highlights application-oriented materials synthesis and modification covering a wide variety of materials such as plastics, rubber, thermo-set, ceramics, and so forth by various radiations. Features: Explains ionizing and non-ionizing radiation-assisted materials development technologies, for polymers, ceramics, metals, and carbons. Covers radiation-assisted synthesis, processing, and modification of all kinds of materials. Provides comparative studies, merits, demerits, and applications very systematically. Criss-crosses polymers science and technology, radiation technology, advanced materials technology, biomaterials technology, and so forth. Includes a section on 3D printing by LASER melting of CoCr alloys. This book is aimed at researchers and graduate students in materials science, radiation chemistry and physics, and polymer and other materials processing.

Author: M. Chen
Publisher: IOS Press
ISBN: 1643683233
Category : Technology & Engineering
Languages : en
Pages : 988

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Book Description
Keeping up to date with advances in material science and applied engineering is essential for those working in the field if they are to understand and tackle the challenges they face in an efficient manner and adopt the best and most appropriate solutions available. This book presents the proceedings of MMSE 2022, the 8th International Conference on Advances in Machinery, Materials Science and Engineering Application, held as a hybrid event (both in-person and online) in Wuhan, China, on 23 and 24 July 2022. For the past 12 years, the MMSE international conferences have collated recent advances and experiences, identified emerging trends in technology and encouraged lively debate between students, specialists, engineers and associations from around the world, all of which have had a positive impact in helping to address the world’s engineering challenges. The book contains 121 papers, selected by means of a rigorous international peer-review process by editors and reviewers from the 215 submissions received. Topics covered include the latest advancements in applied mechanics, intelligent manufacturing technology, mechanical and electromechanical engineering, heat transfer, combustion, advanced materials sciences, industrial applications, applied mathematics, simulation and interdisciplinary engineering. Presenting a wealth of exciting ideas for solving real problems in the real world and opening novel research directions, the book will be of interest to materials specialists and engineers from both academia and industry everywhere.

Author: Juan Casado-Díaz
Publisher: Springer Nature
ISBN: 3030981916
Category : Mathematics
Languages : en
Pages : 119

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Book Description
This book aims the optimal design of a material (thermic or electrical) obtained as the mixture of a finite number of original materials, not necessarily isotropic. The problem is to place these materials in such a way that the solution of the corresponding state equation minimizes a certain functional that can depend nonlinearly on the gradient of the state function. This is the main novelty in the book. It is well known that this type of problems has no solution in general and therefore that it is needed to work with a relaxed formulation. The main results in the book refer to how to obtain such formulation, the optimality conditions, and the numerical computation of the solutions. In the case of functionals that do not depend on the gradient of the state equation, it is known that a relaxed formulation consists of replacing the original materials with more general materials obtained via homogenization. This includes materials with different properties of the originals but whose behavior can be approximated by microscopic mixtures of them. In the case of a cost functional depending nonlinearly on the gradient, it is also necessary to extend the cost functional to the set of these more general materials. In general, we do not dispose of an explicit representation, and then, to numerically solve the problem, it is necessary to design strategies that allow the functional to be replaced by upper or lower approximations. The book is divided in four chapters. The first is devoted to recalling some classical results related to the homogenization of a sequence of linear elliptic partial differential problems. In the second one, we define the control problem that we are mainly interested in solving in the book. We obtain a relaxed formulation and their main properties, including an explicit representation of the new cost functional, at least in the boundary of its domain. In the third chapter, we study the optimality conditions of the relaxed problem, and we describe some algorithms to numerically solve the problem. We also provide some numerical experiments carried out using such algorithms. Finally, the fourth chapter is devoted to briefly describe some extensions of the results obtained in Chapters 2 and 3 to the case of dealing with several state equations and the case of evolutive problems. The problems covered in the book are interesting for mathematicians and engineers whose work is related to mathematical modeling and the numerical resolution of optimal design problems in material sciences. The contents extend some previous results obtained by the author in collaboration with other colleagues.

Author: Julien Yvonnet
Publisher: Springer
ISBN: 3030183831
Category : Computers
Languages : en
Pages : 234

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Book Description
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.​

Author: Bhesh Bhandari
Publisher: John Wiley & Sons
ISBN: 1118373928
Category : Technology & Engineering
Languages : en
Pages : 438

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Book Description
Food Materials Science and Engineering covers a comprehensive range of topics in relation to food materials, their properties and characterisation techniques, thus offering a new approach to understanding food production and quality control. The opening chapter will define the scope and application of food materials science, explaining the relationship between raw material structure and processing and quality in the final product. Subsequent chapters will examine the structure of food materials and how they relate to quality, sensory perception, processing attributes and nutrient delivery. The authors also address applications of nanotechnology to food and packaging science. Methods of manufacturing food systems with improved shelf-life and quality attributes will be highlighted in the book.