On the stress overshoot in cluster crystals under shear

Using non-equilibrium molecular dynamics simulations we study the yielding behaviour of a model cluster crystal formed by ultrasoft particles under shear. We investigate the evolution of stress as a function of strain for different shear rates, $\dot{\gamma}$, and temperatures. The stress-strain relation displays a pronounced maximum at the yielding point; the height of this maximum, $\sigma_\text{p}$, increases via a power law with an increasing shear range and tends to saturate to a finite value if the limit shear rate goes to zero (at least within the considered temperature range). Interestingly, this behaviour can be captured by the Herschel-Bulkley type model which, for a given temperature, allows us to predict a static yield stress $\sigma^{0}_\text{p}$ (in the shear rate tending to zero limit), a characteristic timescale $\tau_\text{c}$, and the exponent $\alpha$ of the above-mentioned power-law decay of the $\sigma_\text{p}$ at high shear rates. Furthermore, for different temperatures, the $\sigma_\text{p}$ can be scaled as functions of $\dot{\gamma}$ onto a single master curve when scaled by corresponding $\tau_\text{c}$ and ${\sigma}_\text{p}^{0}$. Moreover, for a given shear rate, $\sigma_\text{p}$ displays a logarithmic dependence on temperature. Again, the $\sigma_\text{p}{-}T$ curves for different shear rates can be scaled on a single logarithmic master curve when scaled by a corresponding fitting parameters.