Mechanics modelling of fern cavitation catapult

Abstract

Cavitation is often regarded as a failure mode in soft materials. An intriguing phenomenon has been recently discovered that fern sporangium can take advantage of drying-induced cavitation instability in annulus cells to disperse spores at an extraordinarily high acceleration. Briefly, the decrease of environmental humidity causes continuous bending of the sporangium and growth of cavities inside the annulus cells, with the elastic energy accumulated in sporangium walls. When the humidity is lower than a critical value, the cavities suddenly expand dramatically inside the cells, causing a quick release of the elastic energy stored in the annular structure. As a result, like a catapult, the sporangium snaps back and ejects the seeds at a high speed. Motivated by the observation, in this article, we study cavitation instability in a similar structure as the sporangium. To simplify the problem, in our model, the mechanics of cells in the sporangium are described by the polymer gel model, while the sporangium wall is modelled as a hyperelastic material. When the environmental humidity is lower than a critical value, through energetic analyses, we can predict the cavitation catapult phenomenon using the model. We hope that our study in this article can provide useful insights into the bio-inspired design of structures which can take advantage of cavitation instability in soft materials.