ABSTRACT
When the composite has TV kinds of fibers embedded in a homogeneous matrix phase, the quantity, £(?,#/(r), can be expressed as
(7)
where the quantities with the index m denote those associated with the matrix phase, C¡}kl is the elastic modulus of the n-th kind fiber and ip„(r) is the characteristic function of the n-th kind fiber phase defined as
(8)
By taking the ensemble average of equation (6) after substituting equation (7), one obtains
(9)
(10)
The following replacement of each quantity in equation (9) is adopted as
(i i)
(12)
(13)
where vn is the volume fraction of the n-th kind fiber, Akiy is a proportionality factor of the displacement gradient inside the n-th kind fiber when a single fiber is placed in a homogeneous medium with the applied at remote distance.
