Homogenization methods for multiscale mechanics
In many physical problems several scales are present in space or time, caused by inhomogeneity of the medium or complexity of the mechanical process. A fundamental approach is to first construct micro-scale models, and then deduce the macro-scale laws and the constitutive relations by properly avera...
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| Médium: | E-kniha |
| Jazyk: | angličtina |
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Singapore
World Scientific Publishing Co. Pte. Ltd
2010
World Scientific Publishing Company WORLD SCIENTIFIC WSPC |
| Vydání: | 1 |
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| ISBN: | 9814282448, 9789814282444 |
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- Homogenization methods for multiscale mechanics -- Acknowledgments -- Preface -- Contents -- 1. Introductory Examples of Homogenization Method -- 2. Diffusion in a Composite -- 3. Seepage in Rigid Porous Media -- 4. Dispersion in Periodic Media or Flows -- 5. Heterogeneous Elastic Materials -- 6. Deformable Porous Media -- 7. Wave Propagation in Inhomogeneous Media -- Subject Index
- Intro -- Contents -- Acknowledgments -- Preface -- 1. Introductory Examples of Homogenization Method -- 1.1. LongWaves in a Layered Elastic Medium -- 1.2. ShortWaves in aWeakly Stratified Elastic Medium -- 1.3. Dispersion of Passive Solute in Pipe Flow -- 1.3.1. Scale Estimates -- 1.3.2. Multiple-Scale Analysis -- 1.3.3. Dispersion Coefficient for Steady Flow -- 1.3.4. Dispersion Coefficient for Oscillatory Flow -- 1.4. Typical Procedure of Homogenization Analysis -- References -- 2. Diffusion in aComposite -- 2.1. Basic Equations for Two Components in Perfect Contact -- 2.2. Effective Equation on the Macroscale -- 2.3. Effective Boundary Condition -- 2.4. Symmetry and Positiveness of Effective Conductivity -- 2.5. Laminated Composites -- 2.6. Bounds for Effective Conductivity -- 2.6.1. First Variational Principle and the Upper Bound -- 2.6.2. Dual Variational Principle and the Lower Bound -- 2.7. Hashin-Shtrikman Bounds -- 2.7.1. Results and Implications -- 2.7.2. Derivation of Hashin-Shtrikman Bounds -- 2.8. Other Approximate Results for Dilute Inclusions -- 2.9. Thermal Resistance at the Interface -- 2.10. Laminated Composites with Thermal Resistance -- 2.10.1. Effective Coefficients -- 2.10.2. Application to Thermal Barrier Coatings -- 2.11. Bounds for the Effective Conductivity -- 2.11.1. Variational Principles and Bounds -- 2.11.2. Application to a Particulate Composite -- 2.12. Chemical Transport in Aggregated Soil -- Appendix 2A. Heat Transfer in a Two-Slab System -- References -- 3. Seepage in Rigid Porous Media -- 3.1. Equations for Seepage Flow and Darcy's Law -- 3.2. Uniqueness of the Cell Boundary-Value Problem -- 3.3. Symmetry and Positiveness of Hydraulic Conductivity -- 3.4. Numerical Computation of the Permeability Tensor -- 3.5. Seepage of a Compressible Fluid -- 3.6. Two-Dimensional FlowThrough a Three-Dimensional Matrix
- 7.5.2. Modulational Instability -- 7.6. Harmonic Generation in Random Media -- 7.6.1. LongWaves in ShallowWater -- 7.6.2. Harmonic Amplitudes -- 7.6.3. Gaussian Disorder -- References -- Additional References on Homogenization Theory -- Subject Index
- 5.7.1. Effective Equations on the Macroscale -- 5.7.2. Variational Principles -- 5.7.3. Bounds for Particulate Composites -- 5.7.4. Size Effects for Particulate Composites -- 5.7.5. Critical Radii for Particulate Composites -- Appendix 5A. Properties of a Tensor of Fourth Rank -- References -- 6. Deformable PorousMedia -- 6.1. Basic Equations for Fluid and Solid Phases -- 6.2. Scale Estimates -- 6.2.1. Quasi-Static Poroelasticity -- 6.2.2. Dynamic Poroelasticity -- 6.3. Multiple-Scale Expansions -- 6.4. Averaged Total Momentum of the Composite -- 6.5. Averaged Mass Conservation of Fluid Phase -- 6.6. Averaged Fluid Momentum -- 6.6.1. Quasi-Static Case -- 6.6.2. Dynamic Case -- 6.7. Time-Harmonic Motion -- 6.8. Properties of the Effective Coefficients -- 6.8.1. Three Identities for General Media -- 6.8.2. Homogeneous and Isotropic Grains -- 6.9. Computed Elastic Coefficients -- 6.10. Boundary-Layer Approximation for Macroscale Problems -- 6.10.1. The Outer Approximation -- 6.10.2. Boundary-Layer Correction -- 6.10.3. Plane RayleighWave in a Poroelastic Half Space -- Appendix 6A. Properties of the Compliance Tensor -- Appendix 6B. Variational Principle for the Elastostatic Problem in a Cell -- References -- 7. Wave Propagation in Inhomogeneous Media -- 7.1. LongWave Through a Compact Cylinder Array -- 7.2. Bragg Scattering of ShortWaves by a Cylinder Array -- 7.2.1. Envelope Equations -- 7.2.2. Dispersion Relation for a DetunedWave Train -- 7.2.3. Scattering by a Finite Strip of Periodic Cylinders -- 7.3. Sound Propagation in a Bubbly Liquid -- 7.3.1. Scale and Order Estimates -- 7.3.2. Near Field of a Spherical Bubble -- 7.3.3. The Intermediate Field -- 7.3.4. The Macroscale Equation -- 7.4. One-Dimensional Sound Through a Weakly Random Medium -- 7.5. Weakly Nonlinear DispersiveWaves in a Random Medium -- 7.5.1. Envelope Equation
- 3.6.1. Governing Equations -- 3.6.2. Homogenization -- 3.6.3. Numerical Results -- 3.7. Porous Media with Three Scales -- 3.7.1. Effective Equations -- 3.7.2. Properties of Hydraulic Conductivity -- 3.7.3. Macropermeability of a Laminated Medium -- 3.8. Brinkman's Modification of Darcy's Law -- 3.9. Effects ofWeak Fluid Inertia -- Appendix 3A. Spatial Averaging Theorem -- References -- 4. Dispersion in Periodic Media or Flows -- 4.1. Passive Solute in a Two-Scale Seepage Flow -- 4.1.1. The Solute Transport Equation and Scale Estimates -- 4.1.2. Macroscale Transport Equation -- 4.1.3. Numerical Computation of Dispersivity -- 4.2. Macrodispersion in a Three-Scale Porous Medium -- 4.2.1. From Micro- to Mesoscale -- 4.2.2. Mass Transport Equation on the Macroscale -- 4.2.3. Second-Order Seepage Velocity -- 4.3. Dispersion and Transport in aWave Boundary Layer Above the Seabed -- 4.3.1. Depth-Integrated Transport Equation in the Boundary Layer -- 4.3.2. Effective Convection Velocity -- 4.3.3. Correlation Coefficients (u(1)i C(1)) and Dispersivity Tensor -- 4.3.4. Dispersion Under a StandingWave in a Lake -- Appendix 4A. Derivation of Convection-Dispersion Equation -- Appendix 4B. An Alternate Form of Macrodispersion Tensor -- References -- 5. Heterogeneous Elastic Materials -- 5.1. Effective Equations on the Macroscale -- 5.2. The Effective Elastic Coefficients -- 5.3. Application to Fiber-Reinforced Composite -- 5.4. Elastic Panels with Periodic Microstructure -- 5.4.1. Order Estimates -- 5.4.2. Two-Scale Analysis and Effective Equations -- 5.4.3. Homogeneous Plate - A Limiting Case -- 5.5. Variational Principles and Bounds for the Elastic Moduli -- 5.5.1. First Variational Principle and the Upper Bound -- 5.5.2. Second Variational Principle and the Lower Bound -- 5.6. Hashin-Shtrikman Bounds -- 5.7. Partially Cohesive Composites