Mechanogeometry of nanowrinkling in biological cholesteric liquid crystal surfaces*

The chiral fibrous architecture is found in chitin (insects), cellulosics (plants), and collagen I (cornea and bone of mammals) and is a solid analogue of that of cholesteric liquid crystals. The surface and interfaces of biological plywoods are distinguished by hierarchical topographies and nanowrinkling. We presented a theory to model the emergence of these surfaces and interfaces using liquid crystal-based shape equations that directly connect material properties with geometric wrinkling. The model applies to liquid crystal precursors of the plywood solid analogues. The theory focuses on wrinkling geometry and mechanics, as well as the mechanogeometry relationships (topology of stress curves and curvature of the wrinkles). We showed that anchoring is a versatile surface morphing mechanism with a rich surface bending stress field, two ingredients behind many potential multifunctionalities.