Three-Dimensional Numerical Modelling of Random Fibrous Networks

Fibrous networks can be found in both natural and artificial systems. This study puts forward an efficient and accurate numerical method which is useful to model fibrous networks in three-dimensional (3D) space. Mathematical modelling of fibres presents a solid way to show the fibre paths. This research focuses on mathematical modelling of fibres in the random fibrous networks called nonwovens as they are one of the most challenging form of fibrous networks to model due to their complex and random microstructure. Reconstructed 3D images of random fibrous structures acquired with X-ray micro-CT system allowed to model them mathematically in the 3D voxel domain. Fibrous structures were modelled with control points using Bezier polynomial functions, which are useful to interpret the geometry of the fibrous networks in 3D. For more accuracy, fibres were modelled from one intersection point to another. Benefits of developing mathematical models of these random fibrous structures were discussed.