Elastic anisotropy of a foam-like solid made of a random network of interconnected fibres

Abstract − Solid networks made by inducing interconnection at fibre contact points in an assembly of fibres usually present a high elastic anisotropy. Particular features of such networks are a negative Poisson ratio behaviour and a significant stiffening contribution due to random triangulation. 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. Two different periodic models are 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 models are assessed by reference to experimental results for a network of metallic fibres. A comparison is also made with a model for truss lattice core representing the fully triangulated case. Assessment is limited by lack of data for networks with larger average out-of-plane fibre orientation