Stiffness of compressed fiber mats

We investigate, using an analytical and a numerical model, the in-plane stiffness of fiber mats. A mat is modeled by randomly depositing thin linear-elastic fibers on top of each other under the influence of an external pressure. The external pressure has the effect of bending the fibers over each other. The fibers are assumed rigidly bonded at contacts. For a low external pressure the stiffness of the mat deviates from that of its two-dimensional projection only by a geometrical factor, and the effective Poisson contraction is close to zero. For higher pressures, stiffness is governed by two competing effects and a maximum appears in the stiffness. The effective Poisson ratio is clearly negative in this range. An approximative analytical description is developed for the stiffness of mats formed under low external pressure. The stiffness is given as a function of only a few parameters: the degree of bonding, the dimensions of the fibers, the elastic constants of the fiber material, and the density of fibers.