Flow heterogeneity and non-linear response in amorphous solids
When imposed to an external load, crystalline materials usually yield along well defined spatial directions which are closely determined by the structure of the crystal and the relative orientation of the applied force with respect to the so called glide planes. In the case of amorphous solids, on the other hand, the lack of long range order and symmetry leads to an isotropic response and the system either resists to the applied load elastically or flows like an isotropic fluid, provided that the external load is sufficiently high. Despite this isotropic response, it has often been observed that amorphous materials may exhibit, under certain circumstances, an inhomogeneous flow pattern even if the macroscopic stress is constant across the system. For example, if a polydisperse suspension of hard sphere-like colloidal particles with a density above its glass transition is sheared in a planar Couette geometry, one observe a complex spatio-temporal flow behaviour regardless of the fact that the stress is constant across the system.
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.