Geometry and Mechanics of Thin Elastic Ribbons

Thin elastic structures such as rods and plates can undergo large displacements without breaking due to the inexpensive energy cost of bending compared to stretching as the thickness vanishes. This ability to dramatically change shape due to confinement, external loads and stimuli is of great interest for functionalization and improving mechanical properties based on geometry rather than chemistry. Ribbons are examples of elongated elastic structures with a strongly anisotropic cross-section making them intermediate between flat flexible filament and narrow thin plate. Due to this specific geometry, ribbons offer an interesting experimental and theoretical playground to explore elastic instabilities under large displacement, near and far from threshold [J. Elast. 119, 137 (2015)]. When stretched and twisted quasi-statically around its axis, elastic ribbons exhibit a wealth of morphologies including single buckle and wrinkles, curled and looped configurations [Phys. Rev. Lett. 111, 174302 (2013)], as well as triangular facets [Soft Matter, 12, 4457 (2016)]. We characterized experimentally the various phases observed varying the twist, tension and the geometry using X-ray imaging and laser profilometry. I will present minimal models incorporating strong geometric non linearities and finite rotation to explain quantitatively the scaling observed for the measured threshold and shapes. Finally, I will present experimental results on the dynamic wrinkling instability of ribbon compressed at a finite rate in a viscous fluid [Phys. Rev. Lett, 119, 088001, (2017)] . The drag induces a dynamic lateral reinforcement of the filament leading to growth of wrinkles that coarsen over time . I will discuss a new dynamical regime where the pattern selection mechanism involves a non-trivial dependence with the loading rate.