Justification of leading order quasicontinuum approximations of strongly nonlinear lattices

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We consider the leading order quasicontinuum limits of a onedimensional granular medium governed by the Hertz contact law under precompression. The approximate model which is derived in this limit is justiéd 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 Schrödinger (NLS) and Korteweg de-Vries (KdV) approximation of FPU models apply directly to a precompressed granular medium in the weakly nonlinear regime.

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