Theory and Examples of Mathematical Modeling for Fine Weave Pierced Fabric

A mathematical abstraction and three-dimensional modeling method of three-dimensional woven fabric structure was developed for the fine weave pierced fabric, taking parametric continuity splines as the track function of tow. Based on the significant parameters of fine weave pierced fabric measured by MicroCT, eight kinds of the three-dimensional digital models of the fabric structure were established with two kinds of tow sections and four kinds of tow trajectory characteristic functions. There is a good agreement between the three-dimensional digital models and real fabric by comparing their structures and porosities. This mathematical abstraction and three-dimensional modeling method can be applied in micro models for sub unit cell and macro models for macroscopic scale fabrics, with high adaptability.