Apparent elastic properties of random fiber networks

Many natural and synthetic materials have fibrous microstructures. In this paper we study computationally the elastic response of three-dimensional random fiber networks with isotropic or preferential fiber orientations. The fibers, represented as linear elastic and isotropic Timoshenko beams, are generated by a Monte Carlo method and joined through rigid fiber-fiber connections. The fiber networks are subjected to displacement boundary conditions, involving uniform in plane normal or shear strains, and their apparent elastic response is evaluated using a finite element method. We investigate the effects of scale (varying fiber length while keeping the specimen size and fiber diameter fixed), fiber orientation, and void volume fraction on the elastic constitutive response of such fiber networks. We find that the apparent stiffness tensor components C₁₁₁₁ and C₁₂₁₂ decrease and have less scatter with increasing scale (and decreasing fiber aspect ratio), higher orientation angle, and higher void volume fraction. Also, the effect of dangling fibers on the void volume fraction is investigated and the resulting elastic response and three ways of estimating the volume fraction of fibers are discussed.