Biomechanics at the Microscale

Male and female genitalia usually evolve rather quickly and yield remarkable diversity in comparison with other characters. Since natural selection influences shapes indirectly through corresponding properties, links between genital features and their functional mechanisms are critically important, in order to understand evolutionary mechanisms of morphological diversity. In this chapter, we numerically modeled hyper-elongated male and female genitalia especially focusing on their physical properties previously observed in cassidine beetles. These male beetles bear an elongated flagellum and female genitalia have a helically coiled spermathecal duct including some reversal turns called knots. The flagellum was demonstrated to have stiffness gradient, which results in a specific mechanical behavior of the entire copulatory system, because the flagellum stiffness properties might influence its motion within the female spermathecal duct. These properties might be partially due to rubber-like protein resilin that is assumed to be an almost perfect elastomer in insects. Resilin is an ideal material for elastic joints that are subjected to repeated cyclical stress. During the lifetime of an insect, resilin shows neither tearing nor fatigue, when stressed within its natural limits. The resilin, almost unique among biological materials returns back to its original position, when the stress is relieved. In this chapter, the simple sphere-on-the-flat geometry was used in a microindentation experiment as one with the most precise determined boundary conditions. Then the mechanical response of resilin was simulated using a generalized Maxwell model with two characteristic time constants and alternatively using a 1D model with just one characteristic time constant. We also applied newly-developed method of dimension reduction allowing us utilization of functional model along with the generalized Maxwell model.