Effective anisotropic properties of fibre network sheets

The effective mechanical properties of plane fibre networks have been derived using discrete homogenization. The resulting equivalent continuum presents strong directional properties, with anisotropy ratios much larger than those that can be found in natural materials. The directionality of the response of the equivalent continuum increases with the slenderness of the fibres, leading to peculiar behaviours, like the formation of narrow bands where the strains present very large gradient. The results of the homogenization have been validated comparing the response of the continuum with the response of “discrete” models, for which each element is modelled as a slender beam, and boundary conditions are accounted for in an exact way.