Mechanical failure of disordered networks derived from frictional packings*

Disordered networks are used widely to study heterogeneous material failure. These structures are inherent to many systems, such as rigid foams or granular materials. In particular, the latter exhibit highly heterogeneous force chain networks that appear to control the response of such media to external perturbations. To characterize these networks, we focus on their mechanical stability. We study the uniaxial response of networks with geometry derived from the force chains observed in granular experiments. We perform experiments on samples created by laser-cutting these networks from acrylic sheets. We find that the mean degree of the network is a control parameter of the failure behavior, which ranges from ductile to brittle. We explain this ductile-brittle transition with rigidity analysis using a frictional (3,3)-pebble game algorithm. We find that the brittle behavior corresponds to the emergence of a percolating rigid cluster occurring at a mean degree close to the isostatic value of a high friction coefficient packing. Moreover, we find that for networks close to the transition point, failure events predominantly occur within the floppy regions between the rigid clusters. To perform an analysis that is not restricted to the networks close to the transition point, we develop a test to study the failure locations. We use a measure taken from network-science tools and capable of identifying likely failure locations in the samples. It consists in comparing the relative importance of the beams of the lattice by studying their geodesic edge betweenness centrality.