Penetration mechanics of a beetle intromittent organ with bending stiffness gradient and a soft tip

Hyper-elongated structures and their penetration are widespread among insects, for example, intromittent organs, ovipositors, and piercing-sucking mouthparts. The penetration of thin structures with high aspect ratio without buckling and rupturing is mechanically very challenging. However, this problem is economically solved in nature, and the solutions might be helpful for, for example, in the development of harmless catheters. We focus on the penetration process of a hyper-elongated structure of a cassidine beetle intromittent organ, termed a flagellum. We applied a three-point bending test for the flagellum to measure its bending stiffness along the entire flagellum. We demonstrated the bending stiffness gradient, in which the basal half is relatively stiff and the apical half is softer, whose good performance during copulation had been previously numerically demonstrated. The stiffness gradient is the result of the flagellum shape, which is cylindrical and tapered toward the tip. Moreover, the curved tip comprises a harder outer curve and a softer inner curve. Considering the findings of preceding studies, the flagellum works in the following way: (i) the bending stiffness gradient supports the flagellum, easily fitting to a shape of a highly coiled spermathecal duct, (ii) the stiffness property of the very tip may make the tip tougher, and (iii) the curled tip and homogeneously cylindrical shape of the organ help the very tip to fit the shape of the spermathecal duct of the female. Our study shows that the apparently simple flagellum penetration is achieved with numerous elaborate mechanical adaptations.