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The response to a localized force provides a sensitive test for differentmodels of stress transmission in granular solids. The elasto-plastic modelstraditionally used by engineers have been challenged by theoretical andexperimental results which suggest a wave-like (hyperbolic) propagation of thestress, as opposed to the elliptic equations of static elasticity. Numericalsimulations of two-dimensional granular systems subject to a localized externalforce are employed to examine the nature of stress transmission in thesesystems as a function of the magnitude of the applied force, the frictionalparameters and the disorder (polydispersity). The results indicate that inlarge systems (typically considered by engineers), the response is close tothat predicted by isotropic elasticity whereas the response of small systems(or when sufficiently large forces are applied) is strongly anisotropic. In thelatter case the applied force induces changes in the contact networkaccompanied by frictional sliding. The larger the coefficient of staticfriction, the more extended is the range of forces for which the response iselastic and the smaller the anisotropy. Increasing the degree of polydispersity(for the range studied, up to 25%) decreases the range of elastic response.This article is an extension of a previously published letter [1].

Effects of Friction and Disorder on the Quasi-Static Response of Granular Solids to a Localized Force