  We consider the leading order quasicontinuum limits of a one-dimensional
granular medium governed by the Hertz contact law under precompression. The
approximate model which is derived in this limit is justified by establishing
asymptotic bounds for the error with the help of energy estimates. The
continuum model predicts the development of shock waves, which are also studied
in the full system with the aid of numerical simulations. We also show that
existing results concerning the Nonlinear Schrodinger (NLS) and Korteweg
de-Vries (KdV) approximation of FPU models apply directly to a precompressed
granular medium in the weakly nonlinear regime.
