An analytical solution for the load distribution along a fibre in a nonwoven network

This paper develops a method to analyse the load distribution along a half fibre in a non-woven or fibre composite where force is transferred into the fibre at any set of discrete contacts. The force transferred at each contact is assumed to be proportional to the displacement of the contact relative to the applied strain field. The constant of proportionality between displacement and force can be set independently for each contact. The cross-sectional area and elastic modulus of each segment between contacts can also be set independently. It was shown that the displacement, due to the applied strain, at each contact could be expressed in terms of the displacement at the last contact at the end of the fibre. As the displacement at the last contact was the sum of the previous contacts, each multiplied by a stress transfer coefficient, the stress distribution along the fibre could be solved analytically. The debonding of fibres from a paper sheet under load was simulated. The fibre load-network strain curve was found to be highly sensitive to the configuration of the crossing points. The method of analysis has application to nonwoven networks such as paper as well as nonwoven fibre composites.