Stiffness of compressed fiber mats

We investigate, using an analytical and a numerical model, the in-plane sti ffness of fiber mats. A mat is modeled by randomly depositing thin linear-e lastic fibers on top of each other under the influence of an external press ure. The external pressure has the effect of bending the fibers over each o ther. The fibers are assumed rigidly bonded at contacts. For a low external pressure the stiffness of the mat deviates from that of its two-dimensiona l projection only by a geometrical factor, and the effective Poisson contra ction is close to zero. For higher pressures, stiffness is governed by two competing effects and a maximum appears in the stiffness. The effective Poi sson ratio is clearly negative in this range. An approximative analytical d escription is developed for the stiffness of mats formed under low external pressure. The stiffness is given as a function of only a few parameters: t he degree of bonding, the dimensions of the fibers, the elastic constants o f the fiber material, and the density of fibers. (C) 2000 American Institut e of Physics. [S0021-8979(00)04522-9].