Contact breaking in frictionless granular packings

We numerically study the breaking of interparticle contact networks in static granular packings of frictionless bidisperse disks that are subjected to vibrations. The packings are created using an isotropic compression protocol at different values of the total potential energy per particle $E_p$. We first add displacements along a single vibrational mode $i$ of the dynamical matrix to a given packing and calculate the minimum amplitude $A_i$ of the perturbation at which the first interparticle contact breaks. We then identify the minimum amplitude $A_{\rm min}$ over all perturbations along each mode and study the distribution of $A_{\rm min}$ from an ensemble of packings at each $E_p$. We then study two-, three-, and multi-mode excitations and determine the dependence of $A_{\rm min}$ on the number of modes that are included in the perturbation.