We study the effective properties of a linear elastic or perfectly viscoplastic composite consisting of a soft matrix reinforced by possibly very stiff fibers. The effective material is characterized by the emergence of a discrepancy between the displacement in the fibers and the overall averaged displacement, giving rise to a concentration strain in the matrix. The effective energy stored in the fibers is a combination of stretching, bending and torsional energies. This work completes and corrects results previously obtained by the author and coworkers, who failed to notice the torsional contribution.