Longitudinal Traction of a Fiber-Reinforced Composite Beam with Debonded Fibers

The present paper is devoted to the study of longitudinal traction problem of a composite beam with debonded fibers but in contact with the matrix. We show, using the behavior results of" debonded" composites obtained in (Berrehili, Y. and J.-J. Marigo, 2013, The homogenized behavior of unidirectional fiber-reinforced composite materials in the case of debonded fibers, Mathematics and Mechanics of Complex Systems sous presse.) and some intuitive remarks on the symmetry of the problem, that when the period of the microstructure is small enough, the displacement field solution is approximated, in the first order, by a explicit displacement field depending on the fineness of the microstructure. Moreover, unlike that found in the literature, this field depends not only on classical homogenized tensor but also new homogenized tensors characterizing the "debonded" composite.