The mechanical and geometrical properties of fibrous structures

Abstract

This thesis deals with both random and regular (woven) fibre networks. An effective medium theory for the tensile stiffness of two-dimensional random fibre networks is presented. The theory is extended to three-dimensional networks with some but not too strong restrictions. This generalisation involves the computationally determined fraction of bonded crossings in the two-dimensional projection of the three-dimensional network. The two-dimensional and three-dimensional versions of the theory are both succesfully tested against numerical simulations. The porosity of the three-dimensional random fibre networks is found to be given by a numerically determined scaling function, which upon rescaling is shown to be similar to the fraction of bonded crossings described above. This function thus seems to determine the entire structure and mechanical behaviour of randomly deposited fibre mats. A numerical model for the mechanical equilibration of woven fibre networks is also presented. Structures generated by this model are tested against industrially manufactured fabrics. This comparison shows that the model gives fairly realistic results, which guarantees its usefulness also in industrial applications.