Geometrical and spatial effects on fiber network connectivity

For fibrous materials such as nonwoven fabrics, paper and paperboards, inter-fiber bonds play a critical role by holding fibers, thus providing internal cohesion. Being a physical phenomenon, inter-fiber bonds occur at every fiber crossing and can be also geometrically detected. In relation to the idea, a statistical geometrical model was developed to investigate the effects of fiber geometry, (i.e. length and cross-sectional properties), spatial distribution, (i.e. location and orientation), and specimen size on fiber network connectivity, which refers to inter-fiber bonds at fiber crossings. In order to generate the fiber network, a geometrical fiber deposition technique was coded in Mathematica technical computing software, which is based on the planar projections and intersections of fibers and provided as supplementary material to the present article. According to this technique, fiber geometries in discrete rectangular prismatic segments were generated by using uniform distributions of the geometrical and spatial parameters and projected onto the transverse plane. Then, projected geometries were trimmed within the transverse boundaries of the specified specimen shape, rectangular prism in this particular study. After this step, fiber crossings were determined through a search algorithm, which was also used as the basis for the fiber spatial regeneration. Thereafter, fibers were accumulated on top of each other by taking fiber crossings into account and eventually fiber networks based on selected properties were formed. By means of the proposed technique, a series of simulation experiments were conducted on paper fiber networks to investigate the correlation between the fiber network connectivity and fiber length, cross-sectional properties, orientation and specimen length, width and thickness.