Evaluation of the out-of-plane response of fiber networks with a representative volume element model

Many natural and synthetic materials have fibrous microstructures, including nonwoven fabrics, paper, and fiberboard. Experimentally evaluating their out-of-plane mechanical behavior can be difficult because of the small thickness compared with the in-plane dimension. To properly predict such properties, network-scale models are required to obtain homogenized material mechanics by considering fiber-scale mechanisms. We demonstrate a three-dimensional representative volume element (RVE) for fiber networks using the finite element method. We first adopted the classical deposition procedure to generate fiber networks with random or preferential fiber orientations and then an artificial compression to achieve the practical fiber volume fraction. The hollow fibers, described with elastic-plastic brick elements, were joined by interface-based cohesive zone elements introduced in all fiber-fiber contact areas. Thereafter, the fiber networks were subjected to displacement boundary conditions, and their apparent mechanical response was evaluated by a homogenized stress. To determine the RVE dimension, we further conducted an RVE size convergence study for the out-of-plane compression and tension (varying specimen length while keeping the specimen thickness constant). Finally, we evaluated the apparent out-of-plane response of the obtained RVE for four loading cases: out-of-plane compression, tension, simple shear, and pure shear. The results show a quite different mechanical behavior of fiber networks between all these out-of-plane loading cases, particularly between tension and compression.