Micromechanics of Defects in Solids

• 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.

'Professor Mura's book may be heartily recommended to those interested in either applying or learning to apply the methods of continuum mechanics to treat defects in the solid state. This monograph could serve as the perfect text for a second-level graduate course with the same title as that of the book.' Journal of Applied Mechanics