Homogenization Methods
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Rainer Glüge
About this book
Almost all materials are inhomogeneous at the microscale. Typical examples are fiber- and grain structures made of anisotropic phases. These cannot be accounted for in detail in engineering calculations. Instead, effective, homogeneous material properties are used. These are obtained from the inhomogeneous structures by homogenization methods. This book provides a structured overview of the analytical homogenization methods, including the most common estimates, bounds, and Fourier methods. The focus is on linear and anisotropic constitutive relationships, like Hookean elasticity and Fourier’s law for thermal conduction. All sections are accompanied by example calculations, including program code that is also available online.
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a structured overview of the most important homogenization methods and
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examples, including program code.
Author / Editor information
Rainer Glüge is a mechanical engineer who studied continuum mechanics, material modelling and homogenization methods at the University of Magdeburg from 2003 to 2021.
Topics
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Frontmatter
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Preface
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Contents
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1 Introduction
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2 Basics
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3 Characterization of microstructure
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4 The initial and boundary value problem of homogenization
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5 Homogenization with the aid of structural mechanics
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6 Estimates in terms of volume fractions
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7 Basic solutions
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8 Reformulations of the homogenization problem: The eigenstrain problem, the polarization problem and influence tensors
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9 Improved estimates based on the Eshelby solution
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10 Percolation bounds
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11 Hashin–Shtrikman variational method
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12 Fourier and Green methods
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13 Orientation averages
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Bibliography
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Index
187
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