Author: John Daniel Beasley
Publisher:
ISBN:
Category :
Languages : en
Pages : 510

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Book Description

Author: Robert V. Kohn
Publisher: SIAM
ISBN: 9780898712469
Category : Technology & Engineering
Languages : en
Pages : 236

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Book Description

Author: Konstantin Z. Markov
Publisher: World Scientific
ISBN: 9789810216443
Category : Technology & Engineering
Languages : en
Pages : 312

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Book Description
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.

Author: Salvatore Torquato
Publisher: Springer Science & Business Media
ISBN: 1475763557
Category : Mathematics
Languages : en
Pages : 720

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Book Description
This accessible text presents a unified approach of treating the microstructure and effective properties of heterogeneous media. Part I deals with the quantitative characterization of the microstructure of heterogeneous via theoretical methods; Part II treats a wide variety of effective properties of heterogeneous materials and how they are linked to the microstructure, accomplished by using rigorous methods.

Author:
Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 400

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Book Description

Author: University of Delawa
Publisher: CRC Press
ISBN: 9780877626992
Category : Technology & Engineering
Languages : en
Pages : 246

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Book Description
Introduction to Anisotropic Elasticity - Special Applications: Mechanics of Anisotropic Materials - Micromodels for Continuous Fiber Composites - Micromodels for Particulate/Discontinuous Fiber Composites - Introduction to Viscoelasticity - Micromodels for Predicting Viscoelastic Behavior - Transport Properties

Author: Xi Frank Xu
Publisher: CRC Press
ISBN: 0429894384
Category : Science
Languages : en
Pages : 306

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Book Description
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.

Author: Werner E. Kohler
Publisher: American Mathematical Soc.
ISBN: 9780821896952
Category : Mathematics
Languages : en
Pages : 516

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Book Description
In recent years, there has been remarkable growth in the mathematics of random media. The field has deep scientific and technological roots, as well as purely mathematical ones in the theory of stochastic processes. This collection of papers by leading researchers provides an overview of this rapidly developing field. The papers were presented at the 1989 AMS-SIAM Summer Seminar in Applied Mathematics, held at Virginia Polytechnic Institute and State University in Blacksburg, Virginia. In addition to new results on stochastic differential equations and Markov processes, fields whose elegant mathematical techniques are of continuing value in application areas, the conference was organized around four themes: Systems of interacting particles are normally viewed in connection with the fundamental problems of statistical mechanics, but have also been used to model diverse phenomena such as computer architectures and the spread of biological populations. Powerful mathematical techniques have been developed for their analysis, and a number of important systems are now well understood. Random perturbations of dynamical systems have also been used extensively as models in physics, chemistry, biology, and engineering. Among the recent unifying mathematical developments is the theory of large deviations, which enables the accurate calculation of the probabilities of rare events. For these problems, approaches based on effective but formal perturbation techniques parallel rigorous mathematical approaches from probability theory and partial differential equations. The book includes representative papers from forefront research of both types. Effective medium theory, otherwise known as the mathematical theory of homogenization, consists of techniques for predicting the macroscopic properties of materials from an understanding of their microstructures. For example, this theory is fundamental in the science of composites, where it is used for theoretical determination of electrical and mechanical properties. Furthermore, the inverse problem is potentially of great technological importance in the design of composite materials which have been optimized for some specific use. Mathematical theories of the propagation of waves in random media have been used to understand phenomena as diverse as the twinkling of stars, the corruption of data in geophysical exploration, and the quantum mechanics of disordered solids. Especially effective methods now exist for waves in randomly stratified, one-dimensional media. A unifying theme is the mathematical phenomenon of localization, which occurs when a wave propogating into a random medium is attenuated exponentially with propagation distance, with the attenuation caused solely by the mechanism of random multiple scattering. Because of the wide applicability of this field of research, this book would appeal to mathematicians, scientists, and engineers in a wide variety of areas, including probabilistic methods, the theory of disordered materials, systems of interacting particles, the design of materials, and dynamical systems driven by noise. In addition, graduate students and others will find this book useful as an overview of current research in random media.

Author: Dominique Jeulin
Publisher: Springer
ISBN: 3709127807
Category : Computers
Languages : en
Pages : 270

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Book Description
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.

Author: Muhammad Sahimi
Publisher: Springer Science & Business Media
ISBN: 0387217053
Category : Mathematics
Languages : en
Pages : 794

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Book Description
This monograph describes and discusses the properties of heterogeneous materials, including conductivity, elastic moduli, and dielectrical constant. The book outlines typical experimental methods, and compares the experimental data and the theoretical predictions. This multidisciplinary book will appeal to applied physicists, materials scientists, chemical and mechanical engineers, chemists, and applied mathematicians.