Computational biomimetics of twisted plywood architectures in fibrous biological composites through chiral liquid crystal self-assembly

摘要

Despite being made of relatively simple materials, fibrous biological composites exhibit remarkable mechanical and physical properties, These hierarchical materials frequently adopt a laminated architecture known as twisted plywood. In most cases this structure is monodomain (i.e. defect free), in which the fibrillar direction rotates around a single axis. However, not infrequently the twisted plywood architecture is found to be polydomain in which case there is multitude of local axis of rotation instead of a single one. In the latter case, the structure presents defects and it is therefore weakened. The origin of the twisted plywood structure is rather complex and has yet to be fully understood. Nevertheless it is strongly believed that liquid crystalline states are involved in its growth process. Indeed, numerous striking structural similarities between fibrous biological composites and these ordered fluid states have been observed and reported. The structure of liquid crystalline materials is known to be greatly dependent on the topology of their bounding surfaces. In this work, a mathematical model based on the Landau-de Gennes theory has been developed to investigate the role played by constraining surfaces in the structural development of a composite material that undergoes a liquid crystalline state during the early stages of its growth. The goal of this study is to investigate the role played by constraining surface on these materials. The numerical simulations qualitatively confirm the hypothesis of Neville, according to which the presence of a constraining surface produces a mechanically effective monodomain structure whereas its absence leads to a weakened polydomain organization. In addition to these results, this approach highlights the role played by modelling in the study of tissue morphogenesis.