A Compromise Reveals Buckling Resistance Strategy of a Naturally Slender Tibia

In nature, slender tibiae of stick insects have an excellent performance in resisting buckling, which raises the questions why the natural evolution chooses the pentagonal shape as the tibiae's cross section to resist buckling? Why is the proximal base round but the distal end pentagonal in adult tibiae? In this study, 3D geometrical models of the tibiae in stick insects are reconstructed aimed at investigating the buckling resistance strategy of the biological composite with different polygonal cross sections. The numerical result is consistent with the experimental observation. Based on large deflection theory, corresponding mechanical models proposed herein can accurately predict the structural response and mechanical behavior at buckling (including both Euler buckling and local buckling). Eventually, with the help of numerical and theoretical analysis, this article might have found the reason for the tibiae of stick insects naturally evolving to form the cross section with a pentagonal shape. In conclusion, the nature's choice of pentagon (S5) cross section could be a best compromise strategy to balance both Euler buckling and local buckling resistance capability. The knowledge gained from this work will inspire the designs of new advanced materials and structures.