bonds $\phi_f$. (a) The fraction of total broken bonds $\phi_{f}$ obtained in simulations of RSN is plotted against $\Delta\alpha$, which quantifies the distance from the BDT predicted by the equal load sharing models. (b) $\phi_{f}$ from RSN versus $\Delta\tilde{\alpha}$. The dashed black line indicates the theoretical prediction for $\phi_f$ according to the MS model (equation \[Da\]) multiplied by a factor $2/3$ to correct for the fraction of vertically aligned bonds. The symbols correspond to the $\lambda_{S}$ value (see legend panel (b)) color-coded according to the amount of disorder $\delta\lambda$ (see legend panel (a)). Error bars indicate standard deviation based on 50 configurations.[]{data-label="fig:BrokenBondRescaling"}](figure6.eps)

The first parameter we explore is the fraction of broken sacrificial bonds at final failure $\phi_f$, as we have a direct prediction from the MS model. In Fig. \[fig:BrokenBondRescaling\](a), we plot $\phi_{f}$ as a function of $\Delta\alpha$, the distance from the BDT as introduced in equation \[Da\] for various amount of disorder $\delta\lambda$. Clearly, we see a strong increase in the number of broken bonds upon going from the brittle to the ductile regime. For $\delta\lambda=0$ we observe that all data points collapse on a step function exactly at the BDT, $\Delta\alpha=0$. When disorder is introduced, the transition 