This paper is devoted to the analysis of the homogenized behavior of unidirectional
composite materials once the fibers are debonded from (but still in contact with) the
matrix. This homogenized behavior is built by an asymptotic method in the
framework of the homogenization theory. The main result is that the homogenized
behavior of the debonded composite is that of a generalized continuous medium with
an enriched kinematics. Indeed, besides the usual macroscopic displacement field, the
macroscopic kinematics contains two other scalar fields. The former one corresponds
to the displacement of the matrix whereas the two latter ones correspond to the
sliding and the rotation of the debonded fibers with respect to the matrix.
Accordingly, new homogenized coefficients and new coupled equilibrium
equations appear. This problem is addressed in a linear elastic three-dimensional
setting.