Flow heterogeneity and non-linear response in amorphous solids
Recently, it has been suggested that a coupling mechanism between fluctuations of the local colloid concentration (density) and shear rate fluctuations may explain this spatial heterogeneity of the shear rate. In order to test this shear concentration coupling (SCC) theory, we have performed event driven molecular dynamics simulations of a hard sphere glass. First of all, our simulations reveal a complex -and essentially fluctuating- spatio-temporal behaviour (figure 1, upper raw). At the same time, the detailed information obtained from our simulations allows to test the basic assumptions underlying the SCC theory. For example, as the name already suggests, SCC assumes a direct coupling between fluctuations of density and shear rate. In particular, the theory says that an increase of density gives rise to a decrease of shear rate and vice versa. Indeed, the existence of a correlation between fluctuations of density and shear rate is confirmed by our simulations (figure 1, bottom left). As a further test, we have verified to which extent the predictions of the shear concentration coupling theory is in line with our observations of a heterogeneous flow behaviour (figure 1, bottom right). However, a more detailed study regarding the time scale and amplitude of fluctuations reveals that these quantities do not behave as expected from the SCC theory (not shown here).
Thus, some parts of our observations are in favour of the shear concentration coupling mechanism but other features reveal a serious inconsistency within the SCC theory. In addition to this test of the SCC theory, our results also suggest that, at least for hard sphere glasses, no steady state shear banded solution exists. Due to limitations in the available time and length scales, however, no conclusion could so far be made on this issue. Future studies of this issue are thus necessary in order to answer this interesting open question.