On the tensile response of formed fiber networks with low areal density

Fiber networks are ubiquitous. The networks of interest to this study are distinguished from the widely studied planar random fiber networks (RFN) by their low areal density (grammage), preferential orientation, and fiber curl. Oriented networks are created through a high speed manufacturing process called forming in paper making. A dilute suspension of elastic fibers in water impinges on a moving wire to create a formed network. A discrete element method (DEM) based forming model is developed that incorporates the qualitative effects of fluid shear (preferred fiber orientation) and viscous drag during drainage (fiber conformation to the wire topography). Virtual tensile tests performed on thus formed networks reveal that the tensile response is initially softer due to non-affine deformation, and anisotropic due to preferential orientation. Consequently, an orientation dependent power law with a non-unique exponent emerges for the scaling of modulus and strength with the network density. Tensile test simulations reveal the re-alignment of fibers along the loading direction, and strong strain localization resulting in a few fibers (∼1%) carrying the imposed strain energy. Fiber curl and orientation are observed to govern the degree of non-affine response, stiffness, and strain localization, suggesting that controlling the degree of anisotropy and fiber curl offers the possibility to design networks for specific stiffness and specific strength.