Electrical Transport in Tunably-Disordered Metamaterials

Abstract: Naturally occurring materials are often disordered, with their bulk properties being challenging to predict from the structure, due to the lack of underlying crystalline axes. In this paper, we develop a digital pipeline from algorithmically-created configurations with tunable disorder to 3D printed materials, as a tool to aid in the study of such materials, using electrical resistance as a test case. The designed material begins with a random point cloud that is iteratively evolved using Lloyd's algorithm to approach uniformity, with the points being connected via a Delaunay triangulation to form a disordered network metamaterial. Utilizing laser powder bed fusion additive manufacturing with stainless steel 17-4 PH and titanium alloy Ti-6Al-4V, we are able to experimentally measure the bulk electrical resistivity of the disordered network. The effective resistance of the structure calculated from the combinatorial weighted graph Laplacian is in good agreement with experimental data. However, the effective resistance is sensitive to anisotropy and global network topology, preventing a single network statistic or disorder characterization from predicting global resistivity.