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.

中文翻译：

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具有弯曲刚度梯度和软尖端的甲虫内生器官的穿透力学。

超长结构及其渗透在昆虫中很普遍，例如，内脏器官，产卵器和刺吸式口器。具有高长宽比的薄结构的渗透而不会弯曲和破裂在机械上是非常具有挑战性的。然而，该问题本质上是经济上解决的，并且该解决方案例如对于无害导管的开发可能是有帮助的。我们专注于被称为鞭毛的酪体甲虫内向器官的超长结构的穿透过程。我们对鞭毛进行了三点弯曲测试，以测量其在整个鞭毛上的弯曲刚度。我们证明了弯曲刚度梯度，其中基部的一半相对较硬，而根部的一半较软，先前已通过数值证明了其在交配期间的良好性能。刚度梯度是鞭毛形状的结果，鞭毛形状为圆柱形并朝尖端逐渐变细。此外，弯曲的尖端包括较硬的外部曲线和较软的内部曲线。考虑到先前研究的结果，鞭毛的工作方式如下：（i）弯曲刚度梯度支撑鞭毛，很容易适合高度盘绕的精皮导管的形状；（ii）尖端的刚度可能使尖端更加坚硬，并且（iii）尖端的卷曲和均匀的圆柱形状帮助尖端与女性的精囊管的形状相吻合。我们的研究表明，通过许多精心设计的机械调整，可以实现看似简单的鞭毛穿透。