Effect of the interparticle potential on the yield stress of amorphous solids

A crucially important material parameter for all amorphous solids is the yield stress, which is the value of the stress for which the material yields to plastic flow when it is strained quasistatically at zero temperature. It is difficult in laboratory experiments to determine what parameters of the interparticle potential affect the value of the yield stress. Here we use the versatility of numerical simulations to study the dependence of the yield stress on the parameters of the interparticle potential. We find a very simple dependence on the fundamental scales that characterize the repulsive and attractive parts of the potential, respectively, and offer a scaling theory that collapses the data for widely different potentials and in different space dimensions.

Figure 1

A typical stress vs strain curve. At low strains the stress increases linearly with the slope being the shear modulus. At a strain value of the order of $10\%$ the system undergoes a yielding transition [4]. ${\sigma }_Y$ is the mean stress computed at the elastoplastic steady state obtained after, say, $100\%$ strain (see thick red curve).

Figure 2

A selection of different potentials used to determine the yield stress. Panel A depicts potentials where $r_{\mathrm{co}}/{\lambda }_{\mathit{ij}}$ is the changing length (increasing from left to right). Panel B shows potentials for which $r_{\mathrm{co}}/{\lambda }_{\mathit{ij}}$ remains unchanged as in panel A but with a different attractive behavior.

Figure 3

Stress vs strain curves in two-dimensional systems with the potential shown in Fig. 2, panel A. Note the convergence with increasing $r_{\mathrm{co}}$.

Figure 4

The scaling function $f(s)$ [cf. Eq. (6)], obtained by collapsing the computed ${\sigma }_Y$ values in 2D. Smaller symbols represent lower densities. Potentials used here are of the type found in Fig. 2, panel A.

Figure 5

Plotted are the values of $f(s)$ vs $f(\mathrm{ŝ})$ from the data set presented in Fig. 4, where $\frac{\mathrm{ŝ}}{s}\approx 1$.

Figure 6

The scaling function $f(s)$ [cf. Eq. (6)], obtained by collapsing the computed ${\sigma }_Y$ values in three dimensions using potentials as in Fig. 2, panel A, and $N=1000$. Smaller symbols represent lower densities.

Figure 7

The scaling function $f(s)$ $($cf. Eq. (6)$)$, obtained by collapsing the computed ${\sigma }_Y$ values in 2D. Smaller symbols represent lower densities. Left panel is the collapse of ${\sigma }_Y$ values computed using the “dotted” fashion potentials appearing in Fig. 2, panel B, and the right panel is the collapse of ${\sigma }_Y$ values computed using the “dashed” fashion potentials in the same panel.