Optimization and Plasticity in Disordered Media

We study the plastic yielding of disordered media using the perfectly plastic random fuse model. The yield surfaces are shown to be different from those obtained minimizing the sum of the local yield thresholds, i.e., the so-called minimum "energy" surfaces. As a result, the global yield stress is lower than expected from naive optimization and the difference persists as the sample size increases. At variance with minimum energy surfaces, height-height fluctuations of yield surfaces exhibit multiscaling. We provide a theoretical argument that explains how this behavior arises from the very different nature of the optimization problem in both cases.