Figure 1

(a) Potential energy per particle $E$ for zero-strain configurations, for different values of ${\gamma }_{\max }$ [0.07 ($◯$), 0.08 ($\square$), 0.09 ($\diamond$), 0.1 ($▿$), 0.12 ($▵$), and 0.14 ($☆$)], averaged over different runs with samples of $N=4000$ particles at $T=0.466$ (closed symbols) and $1.0$ (open symbols). The fits are obtained using a stretched exponential model. For the highest values of ${\gamma }_{\max }$, $E$ fluctuates around a plateau after an initial transient, whose value increases with ${\gamma }_{\max }$ and is not dependent on the starting energy (curves with closed and open symbols of the same color and symbol merge), whereas for lower ${\gamma }_{\max }$ the memory of initial conditions is retained. For intermediate values our simulations are not long enough to determine which of the two behaviors eventually holds. (b) Values of characteristic strain ${\tilde{\gamma }}_{\mathrm{acc}}$ (akin to relaxation time) obtained from stretched exponential fits of the energy relaxation like those in (a). The relaxation strain increases as one approaches the transition between the arrested and diffusive regimes. The lines through the data are guides to the eye. Vertical lines indicate critical strain amplitudes ${\gamma }_c$ described in Fig. 3a.Reuse & Permissions

Figure 2

Mean square displacement for configurations, for different ${\gamma }_{\max }$, averaged over different runs with $N=4000$ particles at $T=0.466,1.0$. Symbols are the same as in Fig. 1a. Note the transition between an arrested and diffusive regime as ${\gamma }_{\max }$ is increased.Reuse & Permissions

Figure 3

(a) Values of diffusivity $D$ obtained by fitting the MSD, for the studied system sizes and temperatures. Superimposed on the data are power law fits [Eq. (2)] from which the critical strain ${\gamma }_c$ values obtained [for $N=500,4000,3200$, respectively, for ($T=0.466$, $T=1.0$)] are ($0.115,0.117$), ($0.082,0.084$), and ($0.070,0.073$). The corresponding exponent values $\beta$ are ($0.38,0.36$), ($0.75,0.76$), and ($0.61,0.54$). The inset shows ${\gamma }_c$ vs inverse system size $1/N$. Here ${\gamma }_c$ extrapolates to a nonzero value as $1/N\to 0$. Also shown are the yield strain values ${\gamma }_y$ (black closed symbols) obtained from stress-strain curves at $T=0.466$ as shown in the inset in (b). (b) Stress-strain curves (shown in the inset for $N=4000$) show hysteresis with finite enclosed area that increases with ${\gamma }_{\max }$ at high strain amplitude ${\gamma }_{\max }$. The stress-strain curve obtained under uniform shear is shown for reference, with the vertical line at the peak marking the yield strain ${\gamma }_y$. The areas enclosed by the hysteresis curves are shown in the main panel as a function of ${\gamma }_{\max }$ for all the different system sizes and temperatures studied. The areas, close to zero at low ${\gamma }_{\max }$, become finite above ${\gamma }_c$ (indicated by vertical lines for each system size).Reuse & Permissions

Figure 4

Snapshot of a $N=32000$ configuration obtained in the steady state for ${\gamma }_{\max }=0.08$. Particles in red are those that have undergone a scalar displacement greater than $0.6\sigma$ when the sample is subject to a full shear deformation cycle on the $xy$ plane. The presence of a band is evident.Reuse & Permissions