Non-linear response and shear banding in amorphous solids
There is growing evidence that the flow of driven amorphous solids is not homogeneous, even if the macroscopic stress is constant across the system [1,2]. Recent event driven molecular dynamics simulations of a hard sphere (HS) glass confirm the heterogeneous nature of the flow but at the same time suggest that, at least for HS glasses, no steady state exists . Due to limitations in the available time and length scales, however, no conclusion could be made on this issue. In this study, we plan to address this and related questions via lattice Boltzmann computer simulations of non-Newtonian fluids. The non-Newtonian character of the fluid enters the LB iteration scheme via a shear rate and density dependent relaxation time, thus encoding the shear rate and density dependence of viscosity. Furthermore, the dependence of the hydrostatic pressure on local density and shear rate will be accounted for via a corresponding force term. All the input parameters of the relevant constitutive laws will be taken from the preceding molecular dynamics simulations . The present approach thus will provide a link between microscopic (MD) simulations and macroscopic hydrodynamic response of the system. The reliability of the lattice Boltzmann simulations will be tested by analytic studies of the linear stability phase diagram. As a detailed comparison shows, both the linear stability phase diagram and the dispersion relation for the decay rate of fluctuations in the stable regime will be performed by lattice Boltzmann simulations. Studies of the unstable regime, on the other hand, will allow to study the rich spatio-temporal behaviour of the system over sufficiently long times so that conclusions can be drawn regarding the macro-scale shear banding in amorphous solids.
 F. Varnik, L. Bocquet, J.-L. Barrat, L. Berthier, Phys. Rev. Lett. 90, 095702 (2003).
 R. Besseling, L. Isa, P. Ballesta, G. Petekidis, M.E. Cates, W.C.K. Poon, Phys. Rev. Lett. 105, 268301 (2010).
 S. Mandal, M. Gross, D. Raabe, F. Varnik, Phys. Rev. Lett. 108, 098301 (2012).