Extending The Theory Of Composites To Other Areas Of Science
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Extending The Theory Of Composites To Other Areas Of Science
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Author : Maxence Cassier
language : en
Publisher: Bookbaby
Release Date : 2016
Extending The Theory Of Composites To Other Areas Of Science written by Maxence Cassier and has been published by Bookbaby this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Science categories.
In Chapter 1 we review many of the linear equations of physics, and write them in a canonical form appropriate to the theory of composites. We show how conservation laws, which have played a key role throughout the history of science, can be generalized to equalities which we call "boundary field equalities and inequalities". Chapter 2 reviews the abstract theory of composites, both for the effective tensor and for the associated "Y -tensor". Chapter 3 shows that the problem of finding the Dirichlet-to-Neumann map which governs the response of inhomogeneous bodies, for acoustics, elastodynamics, or electromagnetism can be reformulated as the problem of finding the effective tensor (operator) associated with an abstract problem in the theory of composites. Thus, many tools for bounding effective tensors extend to bounding the Dirichlet-to-Neumann map. Chapter 4, with Maxence Cassier and Aaron Welters, studies in depth the analyticity properties of the Dirichlet-to-Neumann map for electromagnetism, as functions of the variables representing the permittivities and permeabilities of the phases multiplied by the frequency. It is established that the map is an operator-valued Herglotz function of these complex variables. It is anticipated that this will be useful for establishing fundamental limits on performances of devices. Chapter 5 explores bounds on the Dirichlet-to-Neumann map and the associated inverse problem of what can be said about the distribution of materials inside a body from surface measurements, using the connection between Dirichlet-to-Neumann maps and effective tensors in composites. Chapter 6, with Ornella Mattei, derives bounds on the transient response of viscoelastic composites. Significantly, we found that the volume fractions of the phases could almost be exactly determined from measurements of the transient response at certain times. Chapter 7 develops the algebra of finite-dimensional subspace collections. By relaxing the requirement that the subspaces are orthogonal we find that there is a rich algebraic structure associated with subspace collections: operations of addition, subtraction, multiplication, division and substitution can all be defined. Some of these operations are analogous to operations one can do with resistor networks. In Chapter 8 we show this algebra has important uses: in particular by substituting a collection with non- orthogonal subspaces in one with orthogonal subspaces we can accelerate Fast Fourier transform methods for computing the effective tensor and fields in periodic conducting composites, as demonstrated by the numerical results of Moulinec and Suquet. Chapter 9, with Moti Milgrom, looks at the response of multiphase bodies and composites to different fields, which may be electric fields, magnetic fields, temperature gradients, or concentration gradients, which interact in the components due to coupling terms. Chapter 10, with Maxence Cassier and Aaron Welters, develops a rigorous basis for the field equation recursion method for composites of two isotropic phases. This uses a stratification of the Hilbert space, and an inductive procedure, to link together a sequence of associated effective tensors. Chapter 11 shows that by minimising the integral of the square of the Schrodinger equation one can develop a "density functional theory" for excited states in multielectron systems, called "Projection functional theory". Chapter 12 shows one can desymmetrize the Schrödinger equation and develop iterative FFT methods for solving it which at each step only require Fourier transforms in the coordinates of just two electrons. Chapter 13 develops minimization variational principles for Schrodinger's equation for excited states when the energy is complex, and explores certain quadratic functions which have properties that could be useful in analysis. Chapter 14 shows how one can obtain Green's functions for problems with non-self-adjoint operators.
The Theory Of Composites
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Author : Graeme W. Milton
language : en
Publisher: SIAM
Release Date : 2022-12-07
The Theory Of Composites written by Graeme W. Milton and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-07 with Mathematics categories.
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.
Advances In Mathematical Modelling Of Composite Materials
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Author : Konstantin Z. Markov
language : en
Publisher: World Scientific
Release Date : 1994
Advances In Mathematical Modelling Of Composite Materials written by Konstantin Z. Markov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Technology & Engineering categories.
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.
Dynamics Of Lattice Materials
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Author : A. Srikantha Phani
language : en
Publisher: John Wiley & Sons
Release Date : 2017-07-10
Dynamics Of Lattice Materials written by A. Srikantha Phani and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-10 with Technology & Engineering categories.
Provides a comprehensive introduction to the dynamic response of lattice materials, covering the fundamental theory and applications in engineering practice Offers comprehensive treatment of dynamics of lattice materials and periodic materials in general, including phononic crystals and elastic metamaterials Provides an in depth introduction to elastostatics and elastodynamics of lattice materials Covers advanced topics such as damping, nonlinearity, instability, impact and nanoscale systems Introduces contemporary concepts including pentamodes, local resonance and inertial amplification Includes chapters on fast computation and design optimization tools Topics are introduced using simple systems and generalized to more complex structures with a focus on dispersion characteristics
The Theory Of Composites
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Author : Graeme W. Milton
language : en
Publisher: Cambridge University Press
Release Date : 2002-05-06
The Theory Of Composites written by Graeme W. Milton and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-05-06 with Science categories.
The theory of composite materials is the study of partial differential equations with rapid oscillations in their coefficients. Although extensively studied for more than a hundred years, an explosion of ideas in the past four decades has dramatically increased our understanding of the relationship among the properties of the constituent materials, the underlying microstructure of a composite, and the overall effective moduli that govern the macroscopic behavior. This renaissance has been fueled by the technological need for improving our knowledge base of composites, by the advance of the underlying mathematical theory of homogenization, by the discovery of new variational principles, by the recognition of how important the subject is to solving structural optimization problems, and by the realization of the connection with the mathematical problem of quasiconvexification. This book surveys these exciting developments at the frontier of mathematics and presents many new results.
Practical Micromechanics Of Composite Materials
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Author : Jacob Aboudi
language : en
Publisher: Butterworth-Heinemann
Release Date : 2021-08-31
Practical Micromechanics Of Composite Materials written by Jacob Aboudi and has been published by Butterworth-Heinemann this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-31 with Technology & Engineering categories.
Practical Micromechanics of Composite Materials provides an accessible treatment of micromechanical theories for the analysis and design of multi-phased composites. Written with both students and practitioners in mind and coupled with a fully functional MATLAB code to enable the solution of technologically relevant micromechanics problems, the book features an array of illustrative example problems and exercises highlighting key concepts and integrating the MATLAB code. The MATLAB scripts and functions empower readers to enhance and create new functionality tailored to their needs, and the book and code highly complement one another. The book presents classical lamination theory and then proceeds to describe how to obtain effective anisotropic properties of a unidirectional composite (ply) via micromechanics and multiscale analysis. Calculation of local fields via mechanical and thermal strain concentration tensors is presented in a unified way across several micromechanics theories. The importance of these local fields is demonstrated through the determination of consistent Margins of Safety (MoS) and failure envelopes for thermal and mechanical loading. Finally, micromechanics-based multiscale progressive damage is discussed and implemented in the accompanying MATLAB code. Emphasizes appropriate application of micromechanics theories to composite behavior Addresses multiple popular micromechanics theories, which are provided in MATLAB Discusses stresses and strains resulting from realistic thermal and mechanical loading Includes availability of solution manual for professors using the book in the classroom
Scientific And Technical Aerospace Reports
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Author :
language : en
Publisher:
Release Date : 1995
Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Aeronautics categories.
Transformation Thermotics And Extended Theories
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Author : Liu-Jun Xu
language : en
Publisher: Springer Nature
Release Date : 2023
Transformation Thermotics And Extended Theories written by Liu-Jun Xu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Metamaterials categories.
This open access book describes the theory of transformation thermotics and its extended theories for the active control of macroscopic thermal phenomena of artificial systems, which is in sharp contrast to classical thermodynamics comprising the four thermodynamic laws for the passive description of macroscopic thermal phenomena of natural systems. This monograph consists of two parts, i.e., inside and outside metamaterials, and covers the basic concepts and mathematical methods, which are necessary to understand the thermal problems extensively investigated in physics, but also in other disciplines of engineering and materials. The analyses rely on models solved by analytical techniques accompanied by computer simulations and laboratory experiments. This monograph can not only be a bridge linking three first-class disciplines, i.e., physics, thermophysics, and materials science, but also contribute to interdisciplinary development.
An Introduction To Composite Materials
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Author : D. Hull
language : en
Publisher: Cambridge University Press
Release Date : 1996-08-13
An Introduction To Composite Materials written by D. Hull and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-08-13 with Technology & Engineering categories.
This edition has been greatly enlarged and updated to provide both scientists and engineers with a clear and comprehensive understanding of composite materials. In describing both theoretical and practical aspects of their production, properties and usage, the book crosses the borders of many disciplines. Topics covered include: fibres, matrices, laminates and interfaces; elastic deformation, stress and strain, strength, fatigue crack propagation and creep resistance; toughness and thermal properties; fatigue and deterioration under environmental conditions; fabrication and applications. Coverage has been increased to include polymeric, metallic and ceramic matrices and reinforcement in the form of long fibres, short fibres and particles. Designed primarily as a teaching text for final-year undergraduates in materials science and engineering, this book will also interest undergraduates and postgraduates in chemistry, physics, and mechanical engineering. In addition, it will be an excellent source book for academic and technological researchers on materials.
Nuclear Science Abstracts
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Author :
language : en
Publisher:
Release Date : 1975-03
Nuclear Science Abstracts written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-03 with Nuclear energy categories.