Topological soft matter: Kagome lattices with a twist

Abstract

The elastic response of many natural and man-made solid structures, ranging from atomic lattices to bridges, can be understood by viewing them as a network of balls (nodes) connected by springs (compressible struts). The rigidity of the resulting solids depends crucially on the average coordination number of the elastic network, z (i.e., the average number of nodes each node is connected to). This number specifies the average topology of the network. It is a global feature that cannot be changed by smoothly deforming the positions of the nodes; instead, you need to cut the struts.