Universal elastic mechanism for stinger design

Abstract

Living organisms use stingers that vary in length L over eight orders of magnitude, from a few tens of nanometres to several metres, across a wide array of biological taxa. Despite the extreme variation in size, their structures are strikingly similar. However, the mechanism responsible for this remarkable morphological convergence remains unknown. Using basic physical arguments and biomimetic experiments, we reveal an optimal design strategy that links their length, base diameter d0, Young’s modulus E and friction force per unit area μp0. This principle can be framed simply as $${d}_{0} \approx {(\mu {p}_{0}/E)}^{1/3}L$$ . Existing data from measurements on viruses, algae, marine invertebrates, terrestrial invertebrates, plants, terrestrial vertebrates, marine vertebrates—as well as man-made objects such as nails, needles and weapons—are consistent with our predictions. Our results highlight the evolutionary adaptation of mechanical traits to the constraints imposed by friction, elastic stability and cost. The structures of stingers of living organisms are surprisingly similar despite their vastly different lengths. Now, stingers are found to obey a unifying mechanistic principle that characterizes the stingers resistance to buckling.