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Micromechanics of composites : multipole expansion approach /
Micromechanics of Composites: Multipole Expansion Approach is the first book to introduce micromechanics researchers to a more efficient and accurate alternative to computational micromechanics, which requires heavy computational effort and the need to extract meaningful data from a multitude of num...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Amsterdam ; Boston :
Butterworth-Heinemann,
2013.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Half Title; Title Page; Copyright; Contents; Preface; Introduction; 1.1 Motivation for the Work; 1.2 Geometry Models; 1.2.1 Single Inclusion; 1.2.2 Finite Arrays of Inclusions; 1.2.3 Composite Band and Layer; 1.2.4 Representative Unit Cell (RUC) Model; 1.3 Method of Solution; 1.4 Homogenization Problem: Volume vs. Surface Averaging; 1.4.1 Conductivity; 1.4.2 Elasticity; 1.5 Scope and Structure of the Book; Potential Fields of Interacting Spherical Inclusions; 2.1 Background Theory; 2.1.1 Scalar Spherical Harmonics; 2.1.2 Selected Properties of Solid Spherical Harmonics.
- 2.1.3 Spherical Harmonics vs. Multipole Potentials2.2 General Solution for a Single Inclusion; 2.2.1 Multipole Expansion Solution; 2.2.2 Far Field Expansion; 2.2.3 Resolving Equations; 2.3 Particle Coating vs. Imperfect Interface; 2.4 Re-Expansion Formulas for the Solid Spherical Harmonics; 2.4.1 Equally Oriented Coordinate Systems; 2.4.2 Multipole Expansion Theorem; 2.4.3 Arbitrarily Oriented Coordinate Systems; 2.5 Finite Cluster Model (FCM); 2.5.1 Superposition Principle; 2.5.2 FCM Boundary-Value Problem; 2.5.3 Convergence Proof; 2.5.4 Modified Maxwell Method for Effective Conductivity.
- 2.6 Composite Sphere2.6.1 Outer Boundary Condition; 2.6.2 Interface Conditions; 2.6.3 RSV and Effective Conductivity of Composite; 2.7 Half-Space FCM; 2.7.1 Double Fourier Transform of Solid Spherical Harmonics; 2.7.2 Homogeneous Half-Space; 2.7.3 Superposition Sum; 2.7.4 Half-Space Boundary Condition; 2.7.5 Interface Conditions; Periodic Multipoles: Application to Composites; 3.1 Composite Layer; 3.1.1 2P Fundamental Solution of Laplace Equation; 3.1.2 2P Solid Harmonics; 3.1.3 Heat Flux Through the Composite Layer; 3.2 Periodic Composite as a Sandwich of Composite Layers.
- 3.3 Representative Unit Cell Model3.4 3P Scalar Solid Harmonics; 3.4.1 Direct Summation; 3.4.2 Hasimoto's Approach; 3.4.3 2P Harmonics-Based Approach; 3.5 Local Temperature Field; 3.6 Effective Conductivity of Composite; Elastic Solids with Spherical Inclusions; 4.1 Vector Spherical Harmonics; 4.1.1 Vector Surface Harmonics; 4.1.2 Vector Solid Harmonics; 4.2 Scalar and Vector Solid Spherical Biharmonics; 4.3 Partial Solutions of Lame Equation; 4.3.1 Definition; 4.3.2 Properties of Spherical Lame Solutions; 4.4 Single Inclusion in Unbounded Solid; 4.4.1 Far Field Expansion.
- 4.4.2 Resolving Set of Linear Equations4.4.3 Single Inclusion in Viscous Fluid (Stokes's Problem); 4.5 Application to Nanocomposite: Gurtin & Murdoch Theory; 4.5.1 Imperfect Interface Conditions; 4.5.2 Formal Solution; 4.5.3 Single Cavity Under Hydrostatic Far Field Load; 4.5.4 Single Cavity Under Uniaxial Far Field Load; 4.6 Re-Expansion Formulas for the Vector Harmonics and Biharmonics; 4.6.1 Translation of Scalar Biharmonics; 4.6.2 Translation of Vector Harmonics; 4.6.3 Translation of Vector Biharmonics; 4.6.4 Translation of Lame Solutions; 4.6.5 Re-Expansion Due to Rotation.