Micromechanics of Composites: Multipole Expansion Approach

Micromechanics of Composites: Multipole Expansion Approach, Second Edition outlines substantial recent progress in the development of the multipole expansion method and focuses on its application to actual micromechanical problems. The book covers micromechanics topics such as conductivity and elasticity of particulate and fibrous composites, including those with imperfect and partially debonded interfaces, nanocomposites, cracked solids, and more. Complete analytical solutions and accurate numerical data are presented in a unified manner for the multiple inhomogeneity models of finite, semi-, and infinite heterogeneous solids. This new edition has been updated to include the theories and techniques of the multipole expansion method.

Two entirely new chapters covering the conductivity and elasticity of composites with ellipsoidal inhomogeneities and anisotropic constituents have been added. A special emphasis is made on the heterogeneous solids with imperfect interfaces, including the nanoporous and nanocomposite materials.

Gives a systematic account on the multipole expansion method, including its theoretical foundations, analytical and numerical techniques, and a new, dipole moment-based approach to the homogenization problemContains detailed analytical and numerical analyses of a variety of micromechanical multiple inhomogeneity models, providing clear insight into the physical nature of the problems under studyProvides a reliable theoretical framework for developing the full-field based micromechanical theories of a composite’s strength, brittle/fatigue damage development, and other properties

1. Multipole expansion approach 2. Potential fields of interacting spherical inhomogeneities 3. Periodic multipoles and RUC model of composite 4. Elastic solid with spherical inhomogeneities 5. Elasticity of composite half-space, layer and bulk 6. Conductivity of solid with spheroidal inhomogeneities 7. Elastic solid with spheroidal inhomogeneities 8. Composites with transversely isotropic constituents 9. Conductivity of ellipsoidal particle composite 10. Elasticity of ellipsoidal particle composite 11. Circular fiber composite with perfect interfaces 12. Fibrous composite with interface cracks 13. Solids with elliptic inhomogeneities 14. Cracked solids 15. Elliptic fiber composite with imperfect interface 16. Fibrous composite with anisotropic constituents

Appendix A. Spherical harmonics and related theory B. Spheroidal harmonics and related theory C. Ellipsoidal harmonics and related theory D. Selected properties of R? and X? functions E. Elliptic harmonics and related theory