This book stems from a course on Micromechanics that I started about fifteen years ago at Northwestern University. At that time, micromechanics was a rather unfamiliar subject. Although I repeated the course every year, I was never convinced that my notes have quite developed into a final manuscript because new topics emerged constantly requiring revisions, and additions. I finally came to realize that if this is continued, then I will never complete the book to my total satisfaction. Meanwhile, T. Mori and I had coauthored a book in Japanese, entitled Micromechanics, published by Baifu-kan, Tokyo, in 1975. It received an extremely favorable response from students and re­ searchers in Japan. This encouraged me to go ahead and publish my course notes in their latest version, as this book, which contains further development of the subject and is more comprehensive than the one published in Japanese. Micromechanics encompasses mechanics related to microstructures of materials. The method employed is a continuum theory of elasticity yet its applications cover a broad area relating to the mechanical behavior of materi­ als: plasticity, fracture and fatigue, constitutive equations, composite materi­ als, polycrystals, etc. These subjects are treated in this book by means of a powerful and unified method which is called the 'eigenstrain method. ' In particular, problems relating to inclusions and dislocations are most effectively analyzed by this method, and therefore, special emphasis is placed on these topics.

1. General theory of eigenstrains.- 1. Definition of eigenstrains.- 2. Fundamental equations of elasticity.- 3. General expressions of elastic fields for given eigenstrain distributions.- 4. Exercises of general formulae.- 5. Static Green's functions.- 6. Inclusions and inhomogeneities.- 7. Dislocations.- 8. Dynamic solutions.- 9. Dynamic Green's functions.- 10. Incompatibility.- 2. Isotropic inclusions.- 11. Eshelby's solution.- 12. Ellipsoidal inclusions with polynomial eigenstrains.- 13. Energies of inclusions.- 14. Cuboidal inclusions.- 15. Inclusions in a half space.- 3. Anisotropic inclusions.- 16. Elastic field of an ellipsoidal inclusion.- 17. Formulae for interior points.- 18. Formulae for exterior points.- 19. Ellipsoidal inclusions with polynomial eigenstrains in anisotropic media.- 20. Harmonic eigenstrains.- 4. Ellipsoidal inhomogeneities.- 22. Equivalent inclusion method.- 23. Numerical calculations.- 24. Impotent eigenstrains.- 25. Energies of inhomogeneities.- 26. Precipitates and martensites.- 5. Cracks.- 27. Critical stresses of crakes in isotropic media.- 28. Critical stresses of cracks in anisotropic media.- 29. Stress intensity factor for a flat ellipsoidal crack.- 30. Stress intensity factor for a slit-like crack.- 31. Stress concentration factors.- 32. Dugdale-Barenblatt cracks.- 33. Stress intensity factor for an arbitrarily shaped plane crack.- 34. Crack growth.- 6. Dislocations.- 35. Displacement fields.- 36. Stress fields.- 37. Dislocation density tensor.- 38. Dislocation flux tensor.- 39. Energies and forces.- 40. Plasticity.- 41. Dislocation model for fatigue crack initiation.- 7. Material properties and related topics.- 42. Macroscopic average.- Random distribution of inclusions-Mori and Tanaka's theory.- 43. Work-hardening ofdispersion hardened alloys.- 44. Diffusional relaxation of internal and external stresses.- 45. Average elastic moduli of composite materials.- 46. Plastic behavior of polycrystalline metals and composites.- 47. Viscoelasticity of composite materials.- 48. Elastic wave scattering.- 49. Interaction between dislocations and inclusions.- 50. Eigenstrains in lattice theory.- 51. Sliding inclusions.- 52. Recent developments.- Appendix 1.- Einstein summation convention.- Kronecker delta.- Permutation tensor.- Appendix 2.- The elastic moduli for isotropic materials.- Appendix 3.- Fourier series and integrals.- Dirac's delta function and Heaviside's step function.- Laplace transform.- Appendix 4.- Dislocations pile-up.- References.- Author index.