Elastic model of an entangled network of interconnected fibres accounting for negative Poisson ratio behaviour and random triangulation

A model is designed for predicting the elastic constants of a random planar network of interconnected fibres while accounting for two features of such networks: negative Poisson ratio behaviour and random triangulation. The model is based on a periodic network involving both plates and fibres segments, with possibility of reentrant cell shapes. The plates are intended to represent the effect of triangulation. 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 out-of-plane fibre orientation for a fibre volume fraction of 0.20. These predictions are assessed by reference to experimental results for transversely isotropic networks, with very low average out-of-plane fibre orientation, made by sintering compressed mats of stainless steel fibres. A comparison is also made with the predictions of a model for truss lattice core, which is liable to represent the case of a fully triangulated network.