Universal elastic mechanism for stinger design

Modelling biological puncture: a mathematical framework for determining the energetics and scaling

“…Moreover, it appears, based on equation (2.7), that for the same d, a smaller 2θ value leads to less frictional contribution. This speculation agrees with findings in biological puncture with a slender tool [15].…”

“…G c ) be a reasonable estimation for the material toughness G. Moreover, the strength of the puncture tool, e.g. the resistance to fracture, buckling [15] and wear and attrition [54], may also be a significant factor to affect the efficiency and the limitation of puncture-an interesting future direction to explore.…”

“…This biological puncture is used for several functions including prey capture [2,8,13], defence [7,8] and reproduction [14]. While extremely diverse in materials, scale and functions [3,12,15], biological puncture systems are united by the underlying mechanics of puncture, which should lead to certain shared fundamental morphological and mechanical similarities [12,15]. For example, most organic puncture tools exhibit a tapered shape that diminishes in cross-sectional size towards a fixed tip radius.…”

“…These studies often focus on specific puncture cases where damage is produced by either a flat punch or a cylindrical-like tool [16,20,22,26] and are mostly related to medical needle injection [20,22,23] and material characterization [16,24,25]. However, biological puncture tools such as teeth [1], fangs [4] and stingers [15] often resemble tapered, conical shapes, at least at their tips. In this manuscript, we explore a general biomechanical puncture scenario where a conical puncture tool dynamically impacts and generates fracture in a hyperelastic soft material using mathematical tools including continuum mechanics and fracture mechanics.…”

“…In addition to creating a quantitative baseline for puncture energetics, this model should also provide insights into the scaling of biological puncture. Little in organismal biology makes sense without the context of scale [27], and it has been shown that characteristic length scales of a puncture system can play a critical role in determining the amount of energy necessary for puncture [3,4,12,15,17,19,20,22,23,25,28]. Furthermore, characteristic length scales identified in engineered systems are reflected in biology, including puncture tool dimensions related to sharpness [4,19,23,25], the overall size of an organism [3,12], and contact area or volume associated with puncture as functions of depth of puncture [15,17,20,22,28].…”