Self-Consistent Methods for Composites: Vol.1: Static Problems by S.K. KanaunSelf-Consistent Methods for Composites: Vol.1: Static Problems by S.K. Kanaun

Self-Consistent Methods for Composites: Vol.1: Static Problems

byS.K. Kanaun, V. Levin

Paperback | November 25, 2010

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Composite and heterogeneous materials play an important role in modern material engineering and technology. This volume is devoted to the theory of such materials. Static elastic, dielectric, thermo- and electroconductive properties of composite materials reinforced with ellipsoidal homogeneous and multi-layered inclusions, short and long multi-layered fibers, thin hard and soft inclusions, media with cracks and pores are considered. Self-consistent methods are used as the main theoretical tool for the calculation of static and dynamic properties of heterogeneous materials. This book is the first monograph to develop self-consistent methods and apply these to the solution of problems of electromagnetic and elastic wave propagation in matrix composites and polycrystals. Predictions of the methods are compared with experimental data and exact solutions. Explicit equations and efficient numerical algorithms for the calculation of velocities and attenuation coefficients of the mean (coherent) wave fields propagating in composites and polycrystals are presented.The book helps materials engineers to predict properties of heterogeneous materials and to create new composite materials which physical properties are optimal to the exploitation conditions. The results of the book are useful for scholars who work on the theory of composite and heterogeneous media.
Title:Self-Consistent Methods for Composites: Vol.1: Static ProblemsFormat:PaperbackDimensions:400 pages, 9.25 × 6.1 × 0 inPublished:November 25, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048176948

ISBN - 13:9789048176946

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Table of Contents

1. Introduction2. An elastic medium with sources of external and internal stresses 2.1 Medium with sources of external stresses 2.2 Medium with sources of internal stresses2.3 Discontinuities of elastic fields in a medium with sources of external and internal stresses 2.4 Elastic fields far from the sources 2.5 Notes 3. Equilibrium of a homogeneous elastic medium with an isolated inclusion 3.1 Integral equations for a medium with an isolated inhomogeneity 3.2 Conditions on the interface between two media3.3 Ellipsoidal inhomogeneity3.4 Ellipsoidal inhomogeneity in a constant external field 3.5 Inclusion in the form of a plane layer 3.6 Spheroidal inclusion in a transversely isotropic medium 3.7 Crack in an elastic medium3.8 Elliptical crack 3.9 Radially heterogeneous inclusion 3.9.1 Elastic fields in a medium with a radially heterogeneous inclusion 3.9.2 Thermoelastic problem for a medium with a radially heterogeneous inclusion 3.10 Multi-layered spherical inclusion 3.11 Axially symmetric inhomogeneity in an elastic medium 3.12 Multi-layered cylindrical inclusion 3.13 Notes 4. Thin inclusion in a homogeneous elastic medium 4.1 External expansions of elastic fields 4.2 Properties of potentials (4.4) and (4.5) 4.3 External limit problems for a thin inclusion 4.3.1 Thin soft inclusion 4.3.2 Thin hard inclusion 4.4 Internal limiting problems and the matching procedure 4.5 Singular models of thin inclusions 4.6 Thin ellipsoidal inclusions 4.7 Notes 5. Hard fiber in a homogeneous elastic medium 5.1 External and internal limiting solutions 5.2 Principal terms of the stress field inside a hard fiber 5.3 Stress fields inside fibers of various forms 5.3.1 Cylindrical fiber 5.3.2 Prolate ellipsoidal fiber 5.3.3 Fiber in the form of a double cone 5.4 Curvilinear fiber 5.5 Notes 6. Thermal and electric fields in a medium with an isolated inclusion 6.1 Fields with scalar potentials in a homogeneous medium with an isolated inclusion6.2 Ellipsoidal inhomogeneity6.2.1 Constant external field 6.2.2 Linear external field 6.2.3 Spheroidal inhomogeneity in a transversely isotropic medium 6.3 Multi-layered spherical inclusion in a homogeneous medium6.4 Thin inclusion in a homogeneous medium 6.5 Axisymmetric fiber in a homogeneous media 7. Homogeneous elastic medium with a set of isolated inclusion 7.1 The homogenization problem 7.2 Integral equations for the elastic fields in a medium with isolated inclusions 7.3 Tensor of the effective elastic moduli7.4 The effective medium method and its versions7.4.1 Differential effective medium method 7.5 The effective field method 7.5.1 Homogeneous elastic medium with a set of ellipsoidal inclusions 7.5.2 Elastic medium with a set of spherically layered inclusion 7.6 The Mon-Tanaka method 7.7 Regular lattices 7.8 Thin inclusions in a homogeneous elastic medium 7.9 Elastic medium reinforced with hard thin flakes or bands 7.9.1 Elastic medium with thin hard spheroids (flakes) of the same orientation 7.9.2 Elastic medium with thin hard spheroids homoge neousl distributed over the orientations7.9.3 Elastic medium with thin hard unidirected bands of the same orientation 7.10 Elastic media with thin soft inclusions and cracks7.10.1 Thin soft inclusions of the same orientation7.10.2 Homogeneous distribution of thin soft inclusions over the orientations 7.10.3 Elastic medium with regular lattices of thin inclusions 7.11 Plane problem for a medium with a set of thin inclusions7.11.1 A set of thin soft elliptical inclusions of the same orientation 7.11.2 Homogeneous distribution of thin inclusions over the orientations 7.11.3 Regular lattices of thin inclusions in plane 7.11.4 A triangular lattice of cracks 7.11.5 Collinear cracks 7.11.6 Vertical row of parallel cracks 7.12 Matrix composites reinforced by short axisymmetric fibers 7. 13 Elastic medium reinforced with unidirectional multi-layered fibers 7.14 Thermoelastic deformation of composites with multi-layered spherical or cylindrical inclusions 7.15 The point defect model in the theory of composite materials 7.16 Effective elastic properties of hybrid composites 7.16.1 Two different populations of inclusions in a homogeneous matrix (hybrid composite) 7.16.2 Two-point correlation functions for a hybrid composite with sets of cylindrical and spheroidal inclusions 7.16.3 Overall elastic moduli of three phase composites 7.17 Conclusions 7.18 Notes 8. Multi-particle interactions in composites 8.1 The effective field method beyond the quasicrystalline approximation 8.2 Mean values of some homogeneous random fields 8.3 General scheme for constructing multi-point statistical moments8.4 The operator of the effective properties 8.5 Pair interactions between inclusions8.6 Notes 9. Thermo and electroconductive properties of composites 9.1 Integral equations for a medium with isolated inclusions 9.2 The effective medium method 9.2.1 Differential effective medium method 9.3 The effective field method 9.3.1 Random set of thin inclusions 9.4 Dielectric properties of composites with high volume concentration of inclusions 9.4.1 The EFM in application to two-phase composites (the quasicrystalline approximation) 9.4.2 The EFM beyond the quasicrystalline approximation 9.4.3 Effective dielectric permittivity in 3D-case 9.4.4 Interaction between two inclusions in the 2D-case 9.4.5 Dielectric properties of the composites in 2D-case 9.4.6 Discussion and conclusion 9.5 Cross-properties relations 9.6 Notes A. Special tensor bases of four rank tensors A.1 E-basis A.2 P-basis A.3 9-basis A.4 R-basis <_a.520_averaging20_the20_elements20_of20_the20_e2c_20_p2c_20_02c_20_and20_r-bases20_0a_a.620_tensor20_bases20_of20_rank20_four20_tensors20_in20_2d-space20_0a_b.20_generalized20_functions20_connected20_with20_the20_green20_function20_of20_static20_elasticity20_0a_b.120_the20_green20_functions20_of20_static20_elasticity20_in20_the20_k-representation20_0a_b.220_the20_green20_functions20_of20_static20_elasticity20_in20_the20_x-representation20_0a_b.320_the20_green20_functions20_of20_static20_elasticity20_in20_2d-case20_0a_b.420_special20_presentation20_of20_the20_k-operator20_0a_c.20_properties20_of20_some20_potentials20_of20_static20_elasticity20_concentrate20_on20_surfaces20_0a_c.120_gauss27_27_20_and20_stokes27_27_20_integral20_theorems20_0a_c.220_derivatives20_of20_the20_double-layer20_potential20_of20_static20_elasticity20_0a_c.320_potentials20_with20_densities20_that20_are20_tensors20_of20_a20_surface20_0a_d.20_transition20_through20_the20_layers20_in20_the20_problems20_of20_thermoelasticity20_for20_multi-layered20_inclusions20_0a_d.120_elastic20_and20_thermoelastic20_problems20_for20_a20_spherical20_multi-layered20_inclusion20_0a_d.220_elastic20_and20_thermoelastic20_problems20_for20_a20_cylindrical20_multi-layered20_inclusion20_0a_e.20_correlation20_functions20_of20_random20_sets20_of20_spherical20_inclusions0a_e.120_the20_percus-yevick20_correlation20_function20_of20_non-penetrating20_sets20_of20_spheres20_in20_the20_3d-case20_0a_e.220_the20_percus-yevick20_correlation20_function20_of20_non-penetrating20_sets20_of20_spheres20_in20_the20_2d-case20_0a_e.320_correlation20_functions20_of20_the20_boolean20_random20_sets20_of20_spheres20_and20_cylinders20_0a_e.3.20_120_random20_models20_of20_two20_populations20_of20_inclusions0a_references0a_ averaging="" the="" elements="" of="" _e2c_="" _p2c_="" _02c_="" and="" r-bases="" a.6="" tensor="" bases="" rank="" four="" tensors="" in="" 2d-space="" b.="" generalized="" functions="" connected="" with="" green="" function="" static="" elasticity="" b.1="" k-representation="" b.2="" x-representation="" b.3="" 2d-case="" b.4="" special="" presentation="" k-operator="" c.="" properties="" some="" potentials="" concentrate="" on="" surfaces="" c.1="" _gauss27_27_="" _stokes27_27_="" integral="" theorems="" c.2="" derivatives="" double-layer="" potential="" c.3="" densities="" that="" are="" a="" surface="" d.="" transition="" through="" layers="" problems="" thermoelasticity="" for="" multi-layered="" inclusions="" d.1="" elastic="" thermoelastic="" spherical="" inclusion="" d.2="" cylindrical="" e.="" correlation="" random="" sets="" e.1="" percus-yevick="" non-penetrating="" spheres="" 3d-case="" e.2="" e.3="" boolean="" cylinders="" e.3.="" 1="" models="" two="" populations="" references="">