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Author Kachanov, Mark, author.

Title Micromechanics of materials, with applications / Mark Kachanov, Igor Sevostianov.

Published Cham : Springer, [2018]


Location Call No. Status
Physical description 1 online resource.
Series Solid mechanics and its applications ; volume 249
Solid mechanics and its applications ; v. 249.
Springer Engineering eBooks 2018 English+International
Bibliography Includes bibliographical references.
Contents Intro; Preface; Contents; 1 Background Results on Elasticity and Conductivity; 1.1 Basic Equations of Linear Elasticity. Elastic Symmetries; 1.2 Energy Principles of Elasticity; 1.2.1 Virtual Changes of State; 1.2.2 The Principle of Virtual Displacements; 1.2.3 The Principle of Virtual Forces; 1.2.4 The Principle of Stationarity of Potential Energy of an Elastic Solid; 1.2.5 The Principle of Stationarity of Complementary Energy of an Elastic Solid; 1.3 Approximate Symmetries of the Elastic Properties; 1.4 A Summary of Algebra of Fourth-Rank Tensors; 1.4.1 Isotropic Fourth-Rank Tensors.
1.4.2 Anisotropic Fourth-Rank Tensors1.4.3 Transversely Isotropic Tensors; 1.4.4 Averaging of Tensors nn and nnnn Over Orientations in Simplest Cases of Orientation Distribution; 1.4.5 Orthotropic Tensors; 1.5 Thermal and Electric Conductivity: Fourier and Ohm's Laws; 1.6 Green's Tensors in Elasticity and Conductivity and Their Derivatives; 1.6.1 General Representation of Green's Tensor in Elasticity; 1.6.2 Isotropic Elastic Material; 1.6.3 Transversely Isotropic Elastic Material.
1.6.4 Green's Tensor for a Monoclinic Material, in the Plane of Elastic Symmetry and in the Direction Normal to It1.6.5 Cubic Symmetry; 1.6.6 Two-Dimensional Anisotropic Elastic Material; 1.6.7 Derivatives of Green's Tensor; 1.6.8 Green's Function in the Conductivity Problem; 1.7 Dipoles, Moments, and Multipole Expansions in Elasticity and Conductivity; 1.7.1 System of Forces Distributed in Small Volume; 1.7.2 Dipole; 1.7.3 Center of Dilatation; 1.7.4 Force Couple; 1.7.5 Center of Rotation; 1.7.6 Multipole Expansion; 1.8 Stress Intensity Factors.
1.9 General Thermodynamics Framework for Transition from Microscale to Macroscopic Constitutive Equations (Rice's Formalism)1.10 Mathematical Analogies Between Elastostatics and Steady-State Heat Flux. Conductivity Analogues of Stress Intensity Factors; 1.11 Discontinuities of the Elastic and Thermal Fields at Interfaces of Two Different Materials; 1.11.1 Stress Discontinuities in the Elasticity Problem; 1.11.2 Flux Discontinuities in the Conductivity Problem; 2 Quantitative Characterization of Microstructures in the Context of Effective Properties.
2.1 Representative Volume Element (RVE) and Related Issues2.1.1 Hill's Condition. Homogeneous Boundary Conditions; 2.1.2 Averages Over Volume and Their Relation to Quantities Accessible on Its Boundary; 2.1.3 Volumes Smaller than RVE; 2.2 The Concept of Proper Microstructural Parameters; 2.3 The Simplest Microstructural Parameters and Their Limitations; 2.4 Microstructural Parameters Are Rooted in the Non-interaction Approximation; 2.5 Property Contribution Tensors of Inhomogeneities; 2.6 Hill's Comparison (Modification) Theorem and Its Implications.
Summary 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.
Other author Sevostianov, Igor, author.
SpringerLink issuing body.
Subject Micromechanics.
Electronic books.
ISBN 9783319762043 (electronic bk.)
3319762044 (electronic bk.)
9783319762036 (hardcover)
3319762036 (hardcover)
Standard Number 10.1007/978-3-319-76204-3