Modelling biological puncture: a mathematical framework for determining the energetics and scaling
Modelling biological puncture: a mathematical framework for determining the energetics and scaling
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DOI：
10.1098/rsif.2022.0559
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发表时间：
2022-10
影响因子：
3.9
通讯作者：
Bingyang Zhang;P. S. Anderson
中科院分区：
文献类型：
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作者：
Bingyang Zhang;P. S. Anderson
生物穿刺系统使用多种形态学工具（刺、齿、刺等）。穿透目标组织，发挥各种功能（捕获猎物、防御、繁殖）。这些系统是由一组基本的物理规则统一起来的，这些规则决定了它们的力学。虽然以前的研究已经说明了在个别系统中的形式功能关系，这些基本规则还没有被正式化。我们提出了一个数学模型，生物穿刺事件的基础上，能量平衡，允许推导出的能量消耗和形状，大小和材料的响应之间的分析标度关系。该模型确定了穿刺过程中三个必要的能量贡献：断裂产生，材料的弹性变形和克服穿透过程中的摩擦。使用有限元分析和实验测试的理论预测进行了验证。不同的缩放关系之间的比较导致释放的断裂能量和变形能量的贡献的比率作为一个系统，结合工具的形状和材料响应的穿刺效率的措施。该模型代表了一个框架，探索生物穿刺系统的多样性，在一个严格的方式，并允许未来的工作，以研究基本物理定律如何影响这些系统的演变。
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.