Scaling properties of three-dimensional random fibre networks

Random fibre networks have unique mechanical properties and appear as the primary building blocks of many biological and structural materials. Although fibre networks are usually three-dimensional in nature, prior studies have mainly used simplistic two-dimensional models to characterize their properties. The present study creates a 3D strain-based nonaffinity measure and investigates the mechanical behaviour and scaling properties of 3D fibre networks. This measure is used to fully examine the influence of primarily characteristic length scales, i.e. mean segment length and bending length, on nonaffine mechanical behaviour of 3D filamentous networks. It is observed that all nonaffinity measure components exhibit a power-law variation with the probing length scale. Furthermore, it is found that while the degree of nonaffinity in both 2D and 3D systems decreases with increasing the probing length scale, the two power-law scaling regimes previously reported for 2D networks do not appear in 3D.