Universal Scaling Laws for Shear Induced Dilation in Frictional Granular Media

Compressed frictional granular matter cannot flow without dilation. Upon forced shearing to generate flow, the amount of dilation may depend on the initial preparation and a host of material variables. On the basis of both experiments and numerical simulations we show that as a result of training by repeated compression-decompression cycles the amount of dilation induced by shearing the system depends only on the shear rate and on the (pre-shearing) packing fraction. Relating the rheological response to structural properties allows us to derive a scaling law for the amount of dilation after $n$ cycles of compression-decompression. The resulting scaling law has a universal exponent that for trained systems is independent of the inter-granules force laws, friction parameters and strain rate. The amplitude of the scaling law is analytically computable, and it depends only on the shear rate and the asymptotic packing fraction.