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: Jerry L Ericksen
Publisher:
ISBN: 9781461386476
Category :
Languages : en
Pages : 284

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Author: Doïna Cioranescu
Publisher: Oxford University Press on Demand
ISBN: 9780198565543
Category : Mathematics
Languages : en
Pages : 262

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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.

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: Andrea Braides
Publisher: Oxford University Press
ISBN: 9780198502463
Category : Mathematics
Languages : en
Pages : 322

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An introduction to the mathematical theory of the homogenization of multiple integrals, this book describes the overall properties of such functionals with various applications ranging from cellular elastic materials to Riemannian metrics.

Author: Julien Yvonnet
Publisher: Springer
ISBN: 3030183831
Category : Computers
Languages : en
Pages : 223

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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: Robert P. Gilbert
Publisher: Chapman and Hall/CRC
ISBN: 9781584887911
Category : Mathematics
Languages : en
Pages : 352

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Book Description
This book provides a thorough introduction to homogenization, a modeling procedure used to describe processes in complicated structures with known microstructures. It first presents the theoretical foundations of this powerful tool of analysis. Building on the theory, the authors explore various types of application problems, including flow in porous media, sound propagation in fluid saturated solids, acoustics of granular material, computational multiscale finite element methods, and interfaces in viscoelastic materials. The book also discusses results in which G-limits have different structures from the initial operators.

Author: Malena I. Español
Publisher: Springer Nature
ISBN: 3031044967
Category : Mathematics
Languages : en
Pages : 514

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Book Description
This volume highlights contributions of women mathematicians in the study of complex materials and includes both original research papers and reviews. The featured topics and methods draw on the fields of Calculus of Variations, Partial Differential Equations, Functional Analysis, Differential Geometry and Topology, as well as Numerical Analysis and Mathematical Modelling. Areas of applications include foams, fluid-solid interactions, liquid crystals, shape-memory alloys, magnetic suspensions, failure in solids, plasticity, viscoelasticity, homogenization, crystallization, grain growth, and phase-field models.

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

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Book Description
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: Doina Cioranescu
Publisher:
ISBN: 9789738433038
Category :
Languages : en
Pages : 129

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