Shear Localization in a Model Glass

Using molecular dynamics simulations, we show that a simple model of a glassy material exhibits the shear localization phenomenon observed in many complex fluids. At low shear rates, the system separates into a fluidized shear band and an unsheared part. The two bands are characterized by a very different dynamics probed by a local intermediate scattering function. Furthermore, a stick-slip motion is observed at very small shear rates. Our results, which open the possibility of exploring complex rheological behavior using simulations, are compared to recent experiments on various soft glasses.

Figure 1

Filled symbols: rescaled velocity profiles, $u(z)/U_{\mathrm{w}\mathrm{a}\mathrm{l}\mathrm{l}}$, from two independent simulation runs. In both cases, the left wall is moved with a constant velocity $U_{\mathrm{w}\mathrm{a}\mathrm{l}\mathrm{l}}=3.33\times {10}^{-3}$ (${\dot{\gamma }}_{\mathrm{t}\mathrm{o}\mathrm{t}}=0.83\times {10}^{-4}$). Because of Galilean invariance, the sheared region may be located at either the moving or immobile wall. Open symbols: rescaled velocity profiles obtained at higher wall velocities $U_{\mathrm{w}\mathrm{a}\mathrm{l}\mathrm{l}}=3.33\times {10}^{-2}$ and $3.33\times {10}^{-1}$ corresponding to overall shear rates of ${\dot{\gamma }}_{\mathrm{t}\mathrm{o}\mathrm{t}}=0.83\times {10}^{-3}$ and $0.83\times {10}^{-2}$. Note that the local shear rate of the sheared region is smaller at smaller $U_{\mathrm{w}\mathrm{a}\mathrm{l}\mathrm{l}}$.

Figure 2

Left panel: Intermediate scattering function, ${\varphi }_q(t;z)$, computed within layers of thickness $dz=2$. From bottom to top, $z=-17,-15,\dots ,15,17$. The temperature is $T=0.2$, and ${\dot{\gamma }}_{\mathrm{t}\mathrm{o}\mathrm{t}}=0.83\times {10}^{-4}$. The vertical dashed line marks the time ${\tau }_0=5754\approx 0.5/{\dot{\gamma }}_{\mathrm{t}\mathrm{o}\mathrm{t}}$. Right panel: plot of ${\varphi }_q({\tau }_0;z)$ (connected diamonds), velocity profile (filled circles), local shear stress ${\sigma }_{xz}(z)$ (connected triangles), normal pressure $P_N(z)$ (open diamonds) , and density profile $\rho (z)$ (connected stars).

Figure 3

Connected diamonds: ${\sigma }_{xz}$ versus $\dot{\gamma }$ under homogeneous flow conditions at $T=0.2$. Connected circles: ${\sigma }_{xz}$ versus ${\dot{\gamma }}_{\mathrm{t}\mathrm{o}\mathrm{t}}$ in the boundary-driven shear flow. The vertical dashed line is an estimate of the global shear rate below which shear localization is expected.

Figure 4

Shear stress versus time for ${\dot{\gamma }}_{\mathrm{t}\mathrm{o}\mathrm{t}}=0.83\times {10}^{-6}$ at $T=0.2$. The stress rises up to a value close to ${\sigma }_y\simeq 0.65$, before suddenly dropping to a value smaller than the one obtained in a homogeneous flow (${\sigma }_{xz}\simeq 0.4)$.