Effect of Local Topological Changes on Resistance in Tunably-Disordered Networks

Disordered materials occur naturally and also provide a broader design space than ordered or crystalline structures. We investigate a two-dimensional disordered network metamaterial constructed from a Delaunay triangulation of an underlying point pattern. Small perturbations in the point pattern induce topological changes. Most notably, the Delaunay edge flip occurs, in which one diagonal of a quadrilateral is replaced by the other. These topological changes can cause substantial jumps in the effective resistance measured diagonally across the network, when located near the source and the sink node. The jumps are explained analytically by showing that the change in effective resistance from edge removal or addition depends on the voltage drop across that edge. However, Delaunay flips have less impact on global resistance measurements and in larger networks. Still, these local topological changes are relevant for finite-sized samples and experimentally-measurable properties such as electrical transport. Our results demonstrate that global characterizations of network disorder may be inadequate for predicting experimentally realizable transport properties in disordered network metamaterials, highlighting the importance of localized regions in material design.