Signatures of the spatial extent of plastic events in the yielding transition in amorphous solids

Amorphous solids are yield stress materials that flow when a sufficient load is applied. Their flow consists of periods of elastic loading interrupted by rapid stress drops, or avalanches, coming from microscopic rearrangements known as shear transformations (STs). Here we show that the spatial extent of avalanches in a steadily sheared amorphous solid has a profound effect on the distribution of local residual stresses that in turn determines the stress drop statistics. As reported earlier, the most unstable sites are located in a flat plateau region that decreases with system size. While the entrance into the plateau is set by the lower cutoff of the mechanical noise produced by individual STs, the departure from the usually assumed power-law (pseudogap) form of the residual stress distribution comes from far field effects related to spatially extended rearrangements. Interestingly, we observe that the average residual stress of the weakest sites is located in an intermediate power-law regime between the pseudogap and the plateau regimes, whose exponent decreases with system size. Our findings imply a new scaling relation linking the exponents characterizing the avalanche size and residual stress distributions.

Automated summary

Amorphous solids exhibit flow behavior under sufficient load, characterized by elastic loading periods interspersed with rapid stress drops, or avalanches, due to microscopic rearrangements known as shear transformations (STs). The spatial extent of these avalanches affects the distribution of local residual stresses and the statistics of stress drops. The study also reveals that the distribution of residual stresses is influenced by far field effects related to spatially extended rearrangements.