Figure 1

Homogeneous deformation at a shear rate of $\dot{\gamma }=1.5\times {10}^{-5}{\mathrm{s}}^{-1}$. (a) Mean square displacement of the quiescent glass without applied shear. The structural relaxation time $\tau$ of the glass is estimated by extrapolating the mean square displacement in the diffusive regime with a line of slope 1 (dashed black line). (b) Displacements of individual particles ($+$) and average displacement (dashed line) along the shear direction during $\delta t=10\min$ of shear. (c) $7\mu \mathrm{m}$ thick reconstruction of the distribution of shear strain after $\delta t=3\min$ of shear. Particle color indicates the value of ${ϵ}_{xz}$. The inset in (c) shows the relative frequency of shear strain magnitudes ${ϵ}_{xz}$ for time intervals $\delta t=3$ (green stars) and 25 min (blue squares). (d) Angle-resolved spatial correlation $C_{{ϵ}_{xz}}$ of the fluctuations of shear strain, in the $x\mathrm{\text{−}}z$ plane. (e) $C_{{ϵ}_{xz}}$ as a function of distance averaged over angular wedges of 10° around the horizontal (red line), the vertical (green line), and the two diagonal directions (blue line). (f) Angle-averaged correlation function $C_{D_{\min }^2}$ as a function of distance in a double-logarithmic representation.Reuse & Permissions

Figure 2

Inhomogeneous deformation at a shear rate of $\dot{\gamma }=1\times {10}^{-4}{\mathrm{s}}^{-1}$. (a) Particle displacements along the shear direction during $\delta t=4\min$ of shear. Dashed red lines are linear fits to the shear profiles for $z<z_l=23\mu \mathrm{m}$ (low shear band) and $z>z_h=28\mu \mathrm{m}$ (high shear band). (b) $7\mu \mathrm{m}$ thick reconstruction of the distribution of incremental shear strain ${ϵ}_{xz}$ during the time interval $\delta t=7\min$. (c) Angle-averaged correlation function $C_{D_{\min }^2}$ as a function of distance $\delta r$, for the low shear band (blue squares), for the high shear band (yellow diamonds), and for homogeneous shear at $\dot{\gamma }=1.5\times {10}^{-5}$ (blue dots) and $3\times {10}^{-5}{\mathrm{s}}^{-1}$ (orange triangles). A least-squares fit to the data gives a slope of $\alpha \sim -1.3\pm 0.1$ (dashed line). (d) Mean square displacement of particles in the low shear band (black stars and line) and high shear band (red dots and line). (e),(f) Angle-resolved spatial correlations of shear strain, $C_{{ϵ}_{xz}}(\delta r)$, in the $x\mathrm{\text{−}}z$ plane, for the low and the high shear bands, respectively. Correlations are computed over a time interval of $\delta t=3\min$.Reuse & Permissions

Figure 3

Evolution of strain correlations during shear band formation. Shear strain correlation functions $C_{{ϵ}_{xz}}$ computed for the entire field of view before (a) and after (b) the manifestation of shear bands. The arrows in (a) indicate the strong correlations in the direction of shear that lead to shear banding in later stages (b).Reuse & Permissions