arXiv:2610.31738v1 Announce Type: new Abstract: In this work, we develop a nonlinear continuum model for wave propagation in two-dimensional granular materials, building on key ideas from Nesterenko's work. Starting from the Hertzian contact law and neglecting contact friction, we derive an effective continuum description through homogenization, assuming spherical, monodisperse grains, local periodicity, and the Cauchy--Born hypothesis. The resulting strain-gradient model depends on both the first and second gradients of the displacement field. We analyse the hyperbolicity of the leading-order system through its eigenvalues and eigenvectors, establishing conditions for hyperbolicity within a restricted deformation domain. The model is solved using an explicit finite-volume method to investigate gravitational settling and wave propagation. We derive analytical expressions for the longitudinal and transverse wave speeds and highlight their dependence on depth. Finally, the predictions of the continuum model are compared with existing discrete-element simulations. This formulation allows several extensions, including more complex packing geometries, contact laws, and large-deformation regimes in which the contact network can evolve.
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