From a mechanical instability perspective a double eyelid is a double-folded thin film structure on a curved substrate, caused by compression as the film "slides" on the substrate. The underlying mechanics issues, in particular the requirements for forming a double folded structure, are studied using a modeling/simulation framework. A minimalist model is employed to explore the wrinkle to fold transition. Refined and enriched models are further developed based on anatomical structures, which demonstrate three critical factors for the formation of double layer folding of the eyelid. First, a crease line in the eyelid is essential where the local bending rigidity is relatively weak. Second, the skin above the crease line should be thin and wide enough. Third, the skin below the crease line should have a relatively large effective stiffness so it can be lifted as a whole when the eyes open. When the eye is opened beyond about 40% of its initial wrinkle wavelength, the double-folded structure emerges. Various types of eyelid morphologies are discussed based on the mechanistic model. The study provides useful insights for surgery, cosmetics, and morphogenesis, as well as microfabrication.
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