  We present large scale computer simulations of the nonlinear bulk rheology of
lamellar phases (smectic liquid crystals) at moderate to large values of the
shear rate (Peclet numbers 10-100), in both two and three dimensions. In two
dimensions we find that modest shear rates align the system and stabilise an
almost regular lamellar phase, but high shear rates induce the nucleation and
proliferation of defects, which in steady state is balanced by the annihilation
of defects of opposite sign. The critical shear rate at onset of this second
regime is controlled by thermodynamic and kinetic parameters; we offer a
scaling analysis that relates the critical shear rate to a critical "capillary
number" involving those variables. Within the defect proliferation regime, the
defects may be partially annealed by slowly decreasing the applied shear rate;
this causes marked memory effects, and history-dependent rheology. Simulations
in three dimensions show instead shear-induced ordering even at the highest
shear rates studied here. This suggests that the critical shear rate shifts
markedly upward on increasing dimensionality. This may in part reflect the
reduced constraints on defect motion, allowing them to find and annihilate each
other more easily. Residual edge defects in the 3D aligned state mostly point
along the flow velocity, an orientation impossible in two dimensions.
