Discrete domain

To model crack propagation and wear formation in the discrete domain, we employ the coarse-grained approach developed by Pham-Ba and Molinari [28], which enables detachment and reattachment of particles thanks to appropriate adhesive forces. The parameters of the interaction forces between particles are determined such that the assembly of several particles exhibits certain mechanical properties (see Ref. [28] and supplementary material). Therefore, employing this contact law enables controlling the macroscopic material properties exhibited by the DEM, which facilitates the matching of material properties between the FEM and DEM. Similarly to Pham-Ba and Molinari [28], we considered the macroscopic material properties of ${\text{SiO}}_2$ (see Table 1) for the DEM and FEM. The critical particle size required by the contact law to achieve an accurate match of macroscopic material properties is $d_{\text{c}}=\text{1.7 nm}$ (see Eq. 16 in supplementary material). The minimum particle size determined by computational constraints is $d_{\text{min}}=\text{0.37 nm}$ (see Eq. 17 in supplementary material). If a particle is smaller than this value, it will interact with more particles than its closest neighbors, increasing the computational cost. Based on these values, we chose a log normal distribution of particle sizes with a mean grain diameter of $d_0=\text{1.3 nm}$, a maximum grain diameter of $d_{\text{max}}=1.2d_0$, a minimum grain diameter of $d_{\text{min}}=0.8d_0$, and a variance of $0.2(d_{\text{max}}-d_{\text{min}})\text{nm}$.

Amorphous silica properties (SiO$_2^{}$)

Considering that a DEM particle is an order of magnitude larger than the bond lengths between atoms in silica (Si–O: 0.16 nm, O–O: 0.26 nm, Si–Si:0.31 nm) [33], Pham-Ba and Molinari [28] already show a significant reduction in computational time by using their DEM contact law compared to MD. To further reduce computational costs and enable modeling of larger domains, a FEM–DEM bridging coupling approach is deemed necessary.