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.
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