  Using full opto-acoustic numerical simulations, we demonstrate enhancement
and suppression of the SBS gain in a metamaterial comprising a subwavelength
cubic array of dielectric spheres suspended in a dielectric background
material. We develop a general theoretical framework and present several
numerical examples using technologically important materials. For As$_2$S$_3$
spheres in silicon, we achieve a gain enhancement of more than an order of
magnitude compared to pure silicon, and for GaAs spheres in silicon, full
suppression is obtained. The gain for As$_2$S$_3$ glass can also be strongly
suppressed by embedding silica spheres. The constituent terms of the gain
coefficient are shown to depend in a complex way on the filling fraction. We
find that electrostriction is the dominant effect behind the control of SBS in
bulk media.
