Mori-Tanaka Method
           
The original method was proposed by Mori and Tanaka [5] in 1973. Further, Benveniste [6] proposed a simpler version of the same model. The key assumption in this model is that the average strain in the inclusion, that is fibre, is related to the average strain in the matrix by a fourth order tensor. This fourth order tensor gives the relation between the uniform strain in the inclusion embedded in an all matrix material. Further, this material is subjected to uniform strain at infinity.
           
The strain concentration factors in fibre are given as

(7.285)

where,

(7.286)

Here,  is the fourth order tensor which relates the average strain in the inclusion to the average strain in the matrix. is Eshelby’s tensor,  and  are the stiffness tensors of fibre and matrix materials, respectively. Dvorak et al [7-9] have given the explicit relations in terms of Hill’s moduli as

(7.287)