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

TL;DR

This paper investigates how the spatial extent of avalanches in sheared amorphous solids influences the distribution of local residual stresses, revealing size-dependent effects and a new scaling relation between avalanche size and stress distributions.

Contribution

It demonstrates that the spatial extent of avalanches affects residual stress distributions and introduces a new scaling relation linking avalanche size and residual stress exponents.

Findings

Residual stress distribution features a system size dependent plateau.

Departure from power-law form is due to far field effects.

Average weakest site stress scales with system size.

Abstract

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 $x$. We find that in this distribution, the most unstable sites are located in a system size dependent plateau. 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 $P(x) \sim x^{\theta}$ comes from far field effects related to spatially extended rearrangements. Interestingly, we observe that the average value of weakest sites $\langle x_{min} \rangle$ 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.