Theory of multilayer woven structures

Multilayer woven fabrics are conventionally represented with the usual weave notation of black and white squares. This notation is based on the top view of the woven fabric. Side view of multilayer woven fabrics contains more important information, namely the routes of warp yarns between layers of weft yarns. In this study, possibilities of woven structures with any numbers of layers and corresponding warp and weft yarns are described. Formulas are derived to describe horizontal, vertical, and diagonal symmetries which lead to identify the fully independent structures. The results serve as the theoretical ground to determine all the possible mechanical properties by using woven reinforcements.