ABSTRACT
An elastic body or a composite contains a variety of inclusions ellipsoidal or a conglomeration of elliptic cracks or fibres of rectangular or other shape .The elastic behaviour of the composite body are changed by the presence of the inclusions or inhomogeneity, and take up not the property of individual constituent materials, but the effective elastic property when external loadings are impressed upon them. The Chapter begins with a discussion of Eshelby’s paper on ellipsoidal inclusions in elastostatic media. This forms the very basis of future works of latter researchers like Wu, Budianski and others. Various self-consistent schemes and energy equivalent method are derived by them in elastostatic cases. In particular Mori Tanaka’s scheme as also the Kuster-Toksoz model are discussed and the connections between them are established. The Chapter ends with a discussion of the dynamic property of elastic moduli from the standpoint of multiple scattering between spherical or ellipsoidal inclusions by Mal, Bose, Datta and others. Also discussed is effective medium method by Kanaun et al. who used the single scattering problem as the basis of calculating the effective dynamic moduli.
