Fractal geometry and multi-scale mechanics of cephalopod shells

菊石类头足类动物的壳中复杂的分形结构，即隔膜，已经成为人们推测的对象超过100年了。重建驱动这些结构迭代进化的功能是一项艰巨的任务，因为没有具有类似结构的现代动物。这意味着隔膜可能反映的生物相互作用或生理学的潜在信息也是未知的，因此它们可能提供的关于菊石进化和灭绝的见解也就丢失了。最普遍的功能解释，连接复杂性的演变，以更深的水栖息地，最近被驳回的结构基础。然而，以前的工作提出了另一种可能的机械功能：抵抗点载荷。该项目旨在通过理论建模，计算力学，3D打印和动态力学分析的结合来探索这种潜在功能。不同头足类壳的粘弹性能和强度将被表征为湿度的函数，因为矿化组织的性质已被证明随相对含水量的变化而变化。这些信息将为物理和虚拟机械测试提供信息，以在不同的形态复杂性下模拟不同代表性间隔形态的强度和屈曲。进一步的测试将通过引入壳的复杂性和壳-隔片系统中的形态变化如何影响强度和屈曲的模型来扩展以前的模型。这项工作的最终目的是解决主要剩余的机械假说隔功能，即是否隔可以反映一种形式的升级。事实上，复杂隔膜的演变可能反映了远洋捕食者不断增加的压力，而不是由栖息地迁移驱动的。间隔复杂性的迭代进化有可能提供关键的见解菊石的进化趋势，只要可以确定其进化的驱动力。

The complex, fractal structures in the shells of ammonoid cephalopods, the septa, have been and the object of speculation for over 100 years. Reconstructing the function that drove the iterative evolution of these structures is a difficult task as there are no modern animals with analogous structures. This means the potential information about biotic interactions or physiology that could be reflected by the septa are likewise unknown, so the insight they might afford about ammonoid evolution and extinction is lost. The most widespread functional explanation, connecting the evolution of complexity to deeper water habitats, has recently been dismissed on a structural basis. However, previous work has suggested another possible mechanical function: resistance to point loads. This project will aim to explore this potential function through a combination of theoretical modeling, computational mechanics, 3D printing, and dynamic mechanical analysis. The viscoelastic properties and strengths of different cephalopod shells will be characterized as a function of humidity as the properties of mineralized tissues have been shown to vary with changes in relative moisture content. This information will inform both physical and virtual mechanical tests to model strength and buckling of different representative septal morphologies at varying morphological complexities. Further tests will expand on previous models by introducing shell complexity and model how morphological variations in the shell-septa system affect strength and buckling. This work will ultimately aim to address the main remaining mechanical hypothesis about septal function, namely whether the septa could reflect a form of escalation. Instead of being driven by habitat migration, the evolution of complex septa may, in fact, reflect increasing pressure from pelagic predators. The iterative evolution of septal complexity has the potential to offer key insights into ammonoid evolutionary trends as long as the driving force for their evolution can be determined.