Is fracture a bigger problem for smaller animals? Force and fracture scaling for a simple model of cutting, puncture and crushing

Abstract

Many of the materials that are challenging for large animals to cut or puncture are also cut and punctured by much smaller organisms that are limited to much smaller forces. Small organisms can overcome their force limitations by using sharper tools, but one drawback may be an increased susceptibility to fracture. We use simple contact mechanics models to estimate how much smaller the diameter of the tips or edges of tools such as teeth, claws and cutting blades must be in smaller organisms in order for them to puncture or cut the same materials as larger organisms. In order to produce the same maximum stress when maximum force scales as the square of body length, the diameter of the tool region that is in contact with the target material must scale isometrically for punch-like tools (e.g. scorpion stings) on thick targets, and for crushing tools (e.g. molars). For punch-like tools on thin targets, and for cutting blades on thick targets, the tip or edge diameters must be even smaller than expected from isometry in smaller animals. The diameters of a small sample of unworn punch-like tools from a large range of animal sizes are consistent with the model, scaling isometrically or more steeply (positively allometric). In addition, we find that the force required to puncture a thin target using real biological tools scales linearly with tip diameter, as predicted by the model. We argue that, for smaller tools, the minimum energy to fracture the tool will be a greater fraction of the minimum energy required to puncture the target, making fracture more likely. Finally, energy stored in tool bending, relative to the energy to fracture the tool, increases rapidly with the aspect ratio (length/width), and we expect that smaller organisms often have to employ higher aspect ratio tools in order to puncture or cut to the required depth with available force. The extra stored energy in higher aspect ratio tools is likely to increase the probability of fracture. We discuss some of the implications of the suggested scaling rules and possible adaptations to compensate for fracture sensitivity in smaller organisms.

The homogenous alternative to biomineralization: Zn- and Mn-rich materials enable sharp organismal “tools” that reduce force requirements

“…We noted above that individual mineral inclusions in crab cuticle, chiton radular teeth, and tooth enamel, are on the scale of microns. This scale is consistent with the sharpest reported biomineralized vertebrate teeth, the teeth of extinct conodonts 107 with 2 μm diameter tips (in contrast with pristine baby mouse teeth, 364 μm 23 , and microchiropteran (bat) molar tips, 25 μm 43 ). The tips of the spider marginal teeth (Mn-HEB) at the center of Fig.…”

How do morphological sharpness measures relate to puncture performance in viperid snake fangs?

“…Intuitively, we consider puncture tools effective at breaking through this integument to be 'sharp'; however, it remains unclear what aspect of morphology determines functional 'sharpness'. The literature on biological cutting/puncturing tools defines morphological sharpness measures in multiple ways: radius of curvature or tip diameter [4][5][6][7][8][9], tip included angle [4,6,7], volume or surface area [7,10], or taper and aspect ratio [9,11]. Measurements of puncture performance typically either measure the performance of models [7,8,11,12] or test the puncturing performance of teeth correlated to a single measure of morphology [4,13].…”

Making a point: shared mechanics underlying the diversity of biological puncture

“…When punctured by multiple tools from different directions, a struggling prey animal cannot shake itself off of one tool without being further embedded on the other. Examples include clutching teeth in sharks (Cappetta, 1987;Ramsay and Wilga, 2007;Whitenack and Motta, 2010;Galloway et al, 2015), felid canines used for throat gripping (Eaton, 1970;Schaller, 1972;Ewer, 1973;Leyhausen, 1979;Van Valkenburgh and Ruff, 1987) and the opposing mandibles found in a number of arthropods (Schofield et al, 2016). These behaviors all involve the application of continuous pressure to keep the puncture tools embedded.…”

“…Recently, a survey of arthropod puncture tools proposed the A B D C perimeter of the cross-section of the tool as a metric ( Fig. 5D; Schofield et al, 2016). Both tip cross-sectional perimeter and tip cross-sectional area have been used by archeologists to categorize prehistoric weaponry (Hughes, 1998;Shea, 2006;Riede, 2009;Shea, 2009, 2011).…”

“…Both tip cross-sectional perimeter and tip cross-sectional area have been used by archeologists to categorize prehistoric weaponry (Hughes, 1998;Shea, 2006;Riede, 2009;Shea, 2009, 2011). Archeologists measure cross-sectional perimeter and area at the widest part of the tool tip, while Schofield et al (2016) measure them 1 mm from the tip of the tool.…”