Stochastic fibre networks: the effects of network structure on percolation and elastic moduli #

Amir Hossein Namdar, Tom Shearer, Alberto Saiani

15:30 Monday in 4Q07.

Part of the Neurons and networks session.

Abstract #

Fibre networks are prevalent in both natural materials, ranging from body tissues to plants, and synthetic materials such as textiles and polymers. Various properties of such materials, such as percolation (whether a contiguous set of fibres spans the network) and elastic moduli, can be studied by modelling them as stochastic networks. In stochastic networks, a given number of fibres are placed in a study domain and their intersection points are defined to act as cross links between the fibres. There is a large body of work dedicated to investigating the behaviour of random networks (a type of stochastic network where individual fibres are placed independently of each other), but departures from randomness, which affect the structure of the network, are poorly studied and understood. Here, to investigate the effects of departures from randomness, we have modified the process of generating the random network by allowing the probability of a fibre appearing and its orientation to depend on its proximity to existing fibres. Our results show that in more homogeneous networks, percolation occurs at a lower fibre density and the mechanical moduli at low fibre densities are higher. Moreover, the rate of change of elastic moduli with respect to fibre density is also studied.