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Abstract An organism’s ability to control the timing and direction of energy flow both within its body and out to the surrounding environment is vital to maintaining proper function. When physically interacting with an external target, the mechanical energy applied by the organism can be transferred to the target as several types of output energy, such as target deformation, target fracture, or as a transfer of momentum. The particular function being performed will dictate which of these results is most adaptive to the organism. Chewing food favors fracture, whereas running favors the transfer of momentum from the appendages to the ground. Here, we explore the relationship between deformation, fracture, and momentum transfer in biological puncture systems. Puncture is a widespread behavior in biology requiring energy transfer into a target to allow fracture and subsequent insertion of the tool. Existing correlations between both tool shape and tool dynamics with puncture success do not account for what energy may be lost due to deformation and momentum transfer in biological systems. Using a combination of pendulum tests and particle tracking velocimetry (PTV), we explored the contributions of fracture, deformation and momentum to puncture events using a gaboon viper fang. Results on unrestrained targets illustrate that momentum transfer between tool and target, controlled by the relative masses of the two, can influence the extent of fracture achieved during high-speed puncture. PTV allowed us to quantify deformation throughout the target during puncture and tease apart how input energy is partitioned between deformation and fracture. The relationship between input energy, target deformation and target fracture is non-linear; increasing impact speed from 2.0 to 2.5 m/s created no further fracture, but did increase deformation while increasing speed to 3.0 m/s allowed an equivalent amount of fracture to be achieved for less overall deformation. These results point to a new framework for examining puncture systems, where the relative resistances to deformation, fracture and target movement dictate where energy flows during impact. Further developing these methods will allow researchers to quantify the energetics of puncture systems in a way that is comparable across a broad range of organisms and connect energy flow within an organism to how that energy is eventually transferred to the environment.
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Modelling biological puncture: a mathematical framework for determining the energetics and scaling
Biological puncture systems use a diversity of morphological tools (stingers, teeth, spines etc.) to penetrate target tissues for a variety of functions (prey capture, defence, reproduction). These systems are united by a set of underlying physical rules which dictate their mechanics. While previous studies have illustrated form–function relationships in individual systems, these underlying rules have not been formalized. We present a mathematical model for biological puncture events based on energy balance that allows for the derivation of analytical scaling relations between energy expenditure and shape, size and material response. The model identifies three necessary energy contributions during puncture: fracture creation, elastic deformation of the material and overcoming friction during penetration. The theoretical predictions are verified using finite-element analyses and experimental tests. Comparison between different scaling relationships leads to a ratio of released fracture energy and deformation energy contributions acting as a measure of puncture efficiency for a system that incorporates both tool shape and material response. The model represents a framework for exploring the diversity of biological puncture systems in a rigorous fashion and allows future work to examine how fundamental physical laws influence the evolution of these systems.
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- Award ID(s):
- 1942906
- PAR ID:
- 10394906
- Date Published:
- Journal Name:
- Journal of The Royal Society Interface
- Volume:
- 19
- Issue:
- 195
- ISSN:
- 1742-5662
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1098/rsif.2022.0559
