Spontaneous formation of permanent shear bands in a mesoscopic model of flowing disordered matter
Abstract
This study proposes a coherent scenario of the formation of permanent shear bands in the flow of yield stress materials. It is a well accepted point of view that flow in disordered media occurs via local plastic events, corresponding to small size rearrangements, that yield a long range stress redistribution over the system. Within a minimalistic mesoscopic model that incorporates these local dynamics, we study the spatial organisation of the local plastic events. The most important parameter in this study is the typical restructuring time needed to regain the original structure after a local rearrangement. In agreement with a recent mean field study [Coussot et al., Eur. Phys. J. E, 2010, 33, 183] we observed the spontaneous formation of permanent shear bands, when this restructuring time is large compared to the typical stress release time in a rearrangement. The bands consist of a large number of plastic events within a solid region that remains elastic. This heterogeneous flow behaviour is different in nature from the transient dynamical heterogeneities that one observes in the small shear rate limit in flow without shear-banding [Martens et al., Phys. Rev. Lett., 2011, 106, 156001]. We analyse in detail the dependence of the shear bands on system size, shear rate and restructuring time. Further, we rationalise the scenario within a mean field version of the spatial model that produces a non monotonous
- This article is part of the themed collection: Bridging the gap between soft and hard colloids