Correlations of plasticity in sheared glasses

In a recent paper [Mandal et al., Phys. Rev. E 88, 022129 (2013)], the nature of spatial correlations of plasticity in hard-sphere glasses was addressed both via computer simulations and in experiments. It was found that the experimentally obtained correlations obey a power law, whereas the correlations from simulations are better fitted by an exponential decay. We here provide direct evidence—via simulations of a hard-sphere glass in two dimensions (2D)—that this discrepancy is a consequence of the finite system size in the 3D simulations. By extending the study to a 2D soft disk model at zero temperature [Durian, Phys. Rev. Lett. 75, 4780 (1995)], the robustness of the power-law decay in sheared amorphous solids is underlined. Deviations from a power law occur when either reducing the packing fraction towards the supercooled regime in the case of hard spheres or changing the dissipation mechanism from contact dissipation to a mean-field-type drag in the case of soft disks.

Figure 1

Correlation of plastic activity in (a),(b) experiments and (c),(d) simulations of hard-sphere glasses. The same data are shown both in double logarithmic (left panel) and semilogarithmic (right panel) scales. The experimental data show robust power-law decay, while the simulations rather show exponential decay.

Figure 2

Angle averaged correlation of plastic activity in 2D simulations of hard disks for various system sizes in (a) double logarithmic and (b) semilogarithmic scale. The packing fraction is $\varphi =0.82>{\varphi }_g\approx 0.80$ (glassy phase). The straight lines are fits to (a) $A{\left(\Delta r\right)}^{-\alpha }$ and (b) $Bexp(-\Delta r/\xi )$ with values of $\alpha$ and $\xi$ as indicated.

Figure 3

Same quantity as in Fig. 2, but for a lower packing fraction of $\varphi =0.77<{\varphi }_g\approx 0.80$ (supercooled state).

Figure 4

Correlation of plastic activity along the flow direction from simulations of a Durian-type model with contact dissipation (CD) and reservoir dissipation (RD) for different densities across the jamming transition (${\varphi }_J\approx 0.843$). The dashed lines and quoted exponents are obtained by fitting $C_{D^2}$ for the CD model to an algebraic decay for $2\le \Delta x/\sigma \le 20$.

Figure 5

(a) Correlation of plastic activity along the flow direction from simulations of a Durian-type model with contact dissipation for different system sizes. (b) Experimental result for a granular suspension.