Meso-structure and processing of three-dimensional braided material based on space group P4 symmetry

A novel three-dimensional (3D) braided material was obtained using group theory. The 3D braided structural unit was found by means of group elements in the point group 4. Based on the symmetry of space group P4, a novel 3D braided material geometry was deduced by transforming the unit. Analyzing the conceivable motion of the yarns, it was found that the geometric structure corresponding to a novel 3D braided material was feasible. The mathematic model for describing the geometry of this novel material was established. The fiber volume fraction of the material was predicted and its value is similar to the traditional four-step 3D braided material. A first prototype of the fabric is produced using manual production.