Abstract
This work addresses a number of fundamental questions regarding the topological description of highly porous three-dimensional materials with bending as the major deformation mecha-nism. This is the dominant deformation mechanism in nanoporous gold as well as in many other open-pore materials, such as architectured materials, foams and isoporous membranes.
The ligament size of nanoporous gold can be nicely tuned via a heat treatment. Recent findings show that this leads to a simultaneous reduction of the connectivity and of the macroscopic mechanical properties [1].
To investigate the role of the connectivity in a more fundamental way, highly efficient finite-element beam models were used with different topologies, ranging from highly coordinated bcc to Gibson–Ashby structures, see Fig. 1(a) [2]. Random cutting enabled a continuous mod-ification of the average coordination number z ranging from the maximum connectivity to the percolation-cluster transition of the 3D network. Via data mining, the interdependencies of topological parameters and relationships between topological parameters with mechanical properties were discovered. It can be shown that the average coordination number 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 ref-erence) to 1.5, close to the percolation-cluster transition, see Fig. 1(b). It was found that 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. The experi-mental data published in [1] support this unexpected finding.
