  We compute the SBS gain for a metamaterial comprising a cubic lattice of
dielectric spheres suspended in a background dielectric material. Theoretical
methods are presented to calculate the optical, acoustic, and opto-acoustic
parameters that describe the SBS properties of the material at long
wavelengths. Using the electromagnetic and strain energy densities we
accurately characterise the optical and acoustic properties of the
metamaterial. From a combination of energy density methods and perturbation
theory, we recover the appropriate terms of the photoelastic tensor for the
metamaterial. We demonstrate that electrostriction is not necessarily the
dominant mechanism in the enhancement and suppression of the SBS gain
coefficient in a metamaterial, and that other parameters, such as the Brillouin
linewidth, can dominate instead. Examples are presented that exhibit an order
of magnitude enhancement in the SBS gain as well as perfect suppression.
