Elastic anisotropy of a transversely isotropic random network of interconnected fibres: non-triangulated network model Original Research Article

Solid networks made by inducing interconnection at fibre contact points in an assembly of fibres usually present a high elastic anisotropy. The paper aims at elucidating the dependence of the stiffness matrix of a random planar fibre network on fibre volume fraction Vf and out-of-plane fibre orientation ψ. A periodic model is designed for representing the network architecture. Bounds for the elastic constants are obtained by calculating volume weighted averages of the elastic properties for periodic networks characterised by a uniform distribution of in-plane fibre orientations. Predictions are derived for the dependence of the in-plane Young’s modulus, out-of-plane Young’s modulus, and in-plane shear modulus on Vf and ψ. The model is assessed by reference to experimental results for a network of metallic fibres. The underestimation of experimental results is presumed to be due to the fact that the model does not account for the effect of triangulation.