Mechanical significance of power-law tapering in biological puncture structures.

Numerous biological taxa have evolved puncturing tools, such as teeth, claws, and spines, for penetration, predation, and defense. Despite differences in material composition and size, these tools exhibit remarkably similar power-law relationships between diameter and distance from the tip. Although the influence of power-law tapering on tool strength has been extensively investigated, its influence on deep puncture mechanics remains poorly understood. Here, we systematically examine the role of power-law conical geometry in puncture performance through combined theoretical and experimental analyses. The results reveal that a taper index of n = 2 maximizes the sensitivity of puncture force to geometric variation dF/dn and provides superior puncture path stability. In addition, a biological puncturing tool-tissue interaction model is developed, and its predictions show good agreement with experimental observations. The analysis further demonstrates that, under shallow penetration conditions, total puncture energy is more sensitive to variations in taper index n. Multi-objective optimization indicates that the predicted optimal taper index is consistent with the tapering characteristics reported for a wide range of biological puncturing structures. These findings suggest that the trade-off between mechanical performance may provide insight into the widespread occurrence of power-law tapering reported in biological pointed structures. The present work also advances the understanding of biological puncture mechanics and form-function relationships and provides mechanical design strategy for biomedical and bioinspired puncture devices.