Connecting Local Yield Stresses with Plastic Activity in Amorphous Solids

In model amorphous solids produced via differing quench protocols, a strong correlation is established between local yield stress measured by direct local probing of shear stress thresholds and the plastic rearrangements observed during remote loading in shear. This purely local measure shows a higher predictive power for identifying sites of plastic activity when compared with more conventional structural properties. Most importantly, the sites of low local yield stress, thus defined, are shown to be persistent, remaining predictive of deformation events even after fifty or more such plastic rearrangements. This direct and nonperturbative approach gives access to relevant transition pathways that control the stability of amorphous solids. Our results reinforce the relevance of modeling plasticity in amorphous solids based on a gradually evolving population of discrete and local zones preexisting in the structure.

Figure 1

(a) Average stress-strain curves for instantaneous (dashed lines) and gradual (continuous lines) quenches. The vertical line is located at ${\gamma }_{xy}=0.07$. (b) Schematic drawing of the local yield stress computation around an atom $i$: region I is fully relaxed while region II is forced to deform following an affine shear deformation in the $\alpha$ direction. Local yield stress maps ${\tau }_y$ [see Eq. (1)] defined for each atom for an instantaneously (c) and a gradually (d) quenched system. The first ten plastic event locations are shown as open black symbols numbered by order of appearance during remote shear loading.

Figure 2

Correlation between the local properties and the locations of the plastic rearrangement as a function of the number of plastic events from the quenched state for instantaneous (a) and gradual (b) quenches. The vertical line corresponds to ${\gamma }_{xy}=0.07$.

Figure 3

Probability distribution function of the local yield stresses for instantaneous (circles) and gradual (squares) quenches. The same quantities are represented in log scale in the inset. The straight lines (shifted for clarity) correspond to power law fits ${\lim }_{{\tau }_y\to 0}P({\tau }_y)\sim {\tau }_y^{\theta }$ from which the tail exponents are estimated.