The statistical analysis of patterns of deformation in flat bonded fibrous networks

Direct microscopic measurements are reported, on the deformation of commercial bonded fibrous networks. The samples include paper and non-woven textiles. Square grid patterns were copied on to the materials and these were photographed during tensile straining. The structures of the deformed patterns were evaluated statistically. In general there was a significant correlation of local deformation with the local areal density of mass. This gave linear regression equations with which the predictions of a statistical theory of elasticity were reasonably consistent. Only a summary of this theory is given here. Its principal concern is with deriving the average over finite regions, of the scalar bulk relation at points. The present experimental evaluation is particularly apt since the modulus at points in a flat, bonded fibrous network is proportional to the areal density of mass at points.