Department of Engineering, University of Campania Luigi Vanvitelli, Via Roma 29, Aversa 81031, Italy.
Division of Invertebrate Paleontology, Florida Museum of Natural History, University of Florida, Gainesville, FL 32618, USA.
J R Soc Interface. 2022 Aug;19(193):20220226. doi: 10.1098/rsif.2022.0226. Epub 2022 Aug 10.
Repeated polygonal patterns are pervasive in natural forms and structures. These patterns provide inherent structural stability while optimizing strength-per-weight and minimizing construction costs. In echinoids (sea urchins), a visible regularity can be found in the endoskeleton, consisting of a lightweight and resistant micro-trabecular meshwork (stereom). This foam-like structure follows an intrinsic geometrical pattern that has never been investigated. This study aims to analyse and describe it by focusing on the boss of tubercles-spine attachment sites subject to strong mechanical stresses-in the common sea urchin . The boss microstructure was identified as a Voronoi construction characterized by 82% concordance to the computed Voronoi models, a prevalence of hexagonal polygons, and a regularly organized seed distribution. This pattern is interpreted as an evolutionary solution for the construction of the echinoid skeleton using a lightweight microstructural design that optimizes the trabecular arrangement, maximizes the structural strength and minimizes the metabolic costs of secreting calcitic stereom. Hence, this identification is particularly valuable to improve the understanding of the mechanical function of the stereom as well as to effectively model and reconstruct similar structures in view of future applications in biomimetic technologies and designs.
重复的多边形图案在自然形态和结构中普遍存在。这些图案在提供固有结构稳定性的同时，优化了强度与重量比，并最小化了建筑成本。在棘皮动物（海胆）中，其内骨骼由轻质且具有高抗性的微小梁网格（stereom）组成，具有明显的规则性。这种泡沫状结构遵循一种内在的几何图案，而这种图案从未被研究过。本研究旨在通过聚焦于常见海胆中承受强烈机械应力的瘤突-棘突附着部位的 boss，对其进行分析和描述。boss 的微观结构被确定为 Voronoi 构造，其与计算的 Voronoi 模型的一致性达到 82%，呈现出六边形多边形的优势，并具有规则的种子分布。这种模式被解释为棘皮动物骨骼结构的一种进化解决方案，采用了轻质的微观结构设计，优化了小梁排列，最大化了结构强度，并最小化了分泌碳酸钙 stereom 的代谢成本。因此，这种鉴定对于提高对 stereom 机械功能的理解以及有效地模拟和重建类似结构具有特别的价值，这些结构考虑到了未来在仿生技术和设计中的应用。
