Data_Sheet_2_Connections Between Topology and Macroscopic Mechanical Properties of Three-Dimensional Open-Pore Materials.ZIP

This work addresses a number of fundamental questions regarding the topological description of materials characterized by a highly porous three-dimensional structure with bending as the major deformation mechanism. Highly efficient finite-element beam models were used for generating data on the mechanical behavior of structures with different topologies, ranging from highly coordinated bcc to Gibson–Ashby structures. Random cutting enabled a continuous modification of average coordination numbers ranging from the maximum connectivity to the percolation-cluster transition of the 3D network. The computed macroscopic mechanical properties–Young's modulus, yield strength, and Poisson's ratio–combined with the cut fraction, average coordination number, and statistical information on the local coordination numbers formed a database consisting of more than 100 different structures. Via data mining, the interdependencies of topological parameters, and relationships between topological parameters with mechanical properties were discovered. A scaled genus density could be identified, which assumes a linear dependency on the average coordination number. Feeding statistical information about the local coordination numbers of detectable junctions with coordination number of 3 and higher to an artificial neural network enables the determination the average coordination number without any knowledge of the fully connected structure. This parameter serves as a common key for determining the cut fraction, the scaled genus density, and the macroscopic mechanical properties. The dependencies of macroscopic Young's modulus, yield strength, and Poisson's ratio on the cut fraction (or average coordination number) could be represented as master curves, covering a large range of structures from a coordination number of 8 (bcc reference) to 1.5, close to the percolation-cluster transition. The suggested fit functions with a single adjustable parameter agree with the numerical data within a few percent error. Artificial neural networks allow a further reduction of the error by at least a factor of 2. All data for macroscopic Young's modulus and yield strength are covered by a single master curve. This leads to the important conclusion that the relative loss of macroscopic strength due to pinching-off of ligaments corresponds to that of macroscopic Young's modulus. Experimental data in literature support this unexpected finding.

本研究围绕以弯曲为主要变形机制的高孔隙率三维结构材料的拓扑描述问题，解答了一系列基础科学议题。本研究采用高效有限元梁模型，生成了不同拓扑结构的力学行为数据集，拓扑结构范围涵盖高配位数体心立方（bcc）结构至吉布森-阿什比（Gibson–Ashby）多孔结构。通过随机切割工艺，可实现平均配位数的连续调控，调控范围覆盖从三维网络的最大连通性直至渗流簇转变点。将计算得到的宏观力学性能——杨氏模量（Young's modulus）、屈服强度（yield strength）与泊松比（Poisson's ratio）——与切割比例、平均配位数以及局部配位数统计信息相结合，构建了包含100余种不同结构的数据库。通过数据挖掘（data mining）技术，研究揭示了拓扑参数间的内在关联，以及拓扑参数与宏观力学性能之间的映射关系。研究识别出一种归一化亏格密度（scaled genus density），其与平均配位数呈线性依赖关系。将配位数不低于3的可检测节点的局部配位数统计信息输入人工神经网络（artificial neural network），即可在无需完整连通结构先验知识的前提下，准确确定平均配位数。该平均配位数可作为通用关键参数，用于推导切割比例、归一化亏格密度以及宏观力学性能。宏观杨氏模量、屈服强度与泊松比对切割比例（或平均配位数）的依赖关系可统一归纳为一条主曲线，覆盖范围从配位数8（体心立方参考结构）直至接近渗流簇转变点的1.5，涵盖了极为宽泛的结构体系。所提出的仅含单个可调参数的拟合函数，与数值模拟数据的相对误差仅为百分之几。借助人工神经网络，可将预测误差进一步降低至少50%。所有宏观杨氏模量与屈服强度的数据均可由单条主曲线统一覆盖。由此得到一项重要结论：因桁条被夹断导致的宏观强度相对损失，与宏观杨氏模量的相对损失完全一致。已有文献报道的实验数据佐证了这一意外发现。