  We report a theoretical study of Stimulated Brillouin Scattering (SBS) in
general anisotropic media, incorporating the effects of both acoustic strain
and local rotation in all calculations. We apply our general theoretical
framework to compute the SBS gain for layered media with periodic length scales
smaller than all optical and acoustic wavelengths, where such composites behave
like homogeneous anisotropic media. We theoretically predict that a layered
medium comprising nanometre-thin layers of silicon and As$_2$S$_3$ glass
possesses a bulk SBS gain of $1.28 \times 10^{-9} \, \mathrm{W}^{-1} \,
\mathrm{m}$. This is more than 500 times larger than the gain coefficient of
silicon, and substantially larger than the gain of As$_2$S$_3$. The enhancement
is due to a combination of roto-optic, photoelastic, and artificial
photoelastic contributions in the composite structure.
