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## Über dieses Buch

This book on micromechanics explores both traditional aspects and the advances made in the last 10–15 years. The viewpoint it assumes is that the rapidly developing field of micromechanics, apart from being of fundamental scientific importance, is motivated by materials science applications.

The introductory chapter provides the necessary background together with some less traditional material, examining e.g. approximate elastic symmetries, Rice’s technique of internal variables and multipole expansions. The remainder of the book is divided into the following parts: (A) classic results, which consist of Rift Valley Energy (RVE), Hill’s results, Eshelby’s results for ellipsoidal inhomogeneities, and approximate schemes for the effective properties; (B) results aimed at overcoming these limitations, such as volumes smaller than RVE, quantitative characterization of “irregular” microstructures, non-ellipsoidal inhomogeneities, and cross-property connections; (C) local fields and effects of interactions on them; and lastly (D) – the largest section – which explores applications to eight classes of materials that illustrate how to apply the micromechanics methodology to specific materials.

## Inhaltsverzeichnis

### Chapter 1. Background Results on Elasticity and Conductivity

Abstract
This chapter summarizes the background material on linear elasticity and conductivity that is used throughout the book. It includes less traditional material on approximate symmetries of the elastic properties and on multipole expansions.
Mark Kachanov, Igor Sevostianov

### Chapter 2. Quantitative Characterization of Microstructures in the Context of Effective Properties

Abstract
In heterogeneous materials, physical fields—stresses, strains, temperature—are variable at microscale. The effective properties interrelate volume averages of these fields. In the context of the elastic properties, this means relations between average stresses and average strains; in the context of thermal conductivity—relations between average temperature gradient and average heat flux; similar definitions apply to other physical properties.
Mark Kachanov, Igor Sevostianov

### Chapter 3. Inclusion and Inhomogeneity in an Infinite Space (Eshelby Problems)

Abstract
Formulation and solution of this problem by Eshelby in [Proc R Soc Lond Ser A 252(1271):561–569, 1969 [125]; Proc R Soc A 241:376–392, 1957 [126]; Elastic inclusions and inhomogeneities. Progress in Solid Mechanics, vol 2. North-Holland, Amsterdam, 1961 [127]) constitutes one of the major advances in solid mechanics of the twentieth century. It has also led to revolutionary changes in mechanics of materials, by establishing a framework for quantitative modeling of phase transformations, effective properties of composites, stress concentrations at inhomogeneities, etc. It has been further advanced in a large number of works and constitutes the basic building block of micromechanics of materials.
Mark Kachanov, Igor Sevostianov

### Chapter 4. Property Contribution Tensors of Inhomogeneities

Abstract
Property contribution tensors introduced in Chap. 2 express contributions of a given inhomogeneity to the effective property of interest, under the assumption that the inhomogeneity is placed into a uniform applied field (that would be uniform within the site of the inhomogeneity in its absence, “homogeneous boundary conditions”, Sect. 2.​1.​1). For the elastic properties, these tensors are the compliance or stiffness contribution tensors, $$\varvec{H}$$ or $$\varvec{N}$$; for the conductive properties—the conductivity or resistivity contribution tensors, $$\varvec{K}$$ or $$\varvec{R}$$.
Mark Kachanov, Igor Sevostianov

### Chapter 5. Effective Properties of Heterogeneous Materials

Abstract
This chapter discusses the problem of effective properties that were defined and briefly discussed in Chap. 2. While focusing on the current state of knowledge, we start with remarks on the pioneering works that date back to nineteenth century; we refer to Markov [336] for in-detail review of history of the subject.
Mark Kachanov, Igor Sevostianov

### Chapter 6. Connections Between Elastic and Conductive Properties of Heterogeneous Materials. Other Cross-Property Relations

Abstract
Cross-property connections for heterogeneous materials belong to the fundamental problems of engineering science and physics. They interrelate changes in different physical properties caused by various inhomogeneities (cracks, pores, inclusions) or, more generally—by the presence of certain microstructure.
Mark Kachanov, Igor Sevostianov

### Chapter 7. Applications to Specific Materials

Abstract
This chapter demonstrates applications of the micromechanics methodology to a number of specific materials. Sections on different materials can be read independently.
Mark Kachanov, Igor Sevostianov

### Backmatter

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