The collective strength of a system of fibers, each having a failure threshold drawn randomly from a distribution, indicates the maximum load carrying capacity of different disordered systems ranging from disordered solids, power-grid networks, to traffic in a parallel system of roads. In many of the cases where the redistribution of load following a local failure can be controlled, it is a natural requirement to find the most efficient redistribution scheme, i.e., following which system can carry the maximum load. We address the question here and find that the answer depends on the mode of loading. We analytically find the maximum strength and corresponding redistribution schemes for sudden and quasistatic loading. The associated phase transition from partial to total failure by increasing the load has been studied. The universality class is found to be dependent on the redistribution mechanism.

• Received 3 March 2015

DOI:https://doi.org/10.1103/PhysRevLett.115.155501