Nonlinear dynamics of contact breaking in jammed solids

We perform computational studies of the response of mechanically stable packings of spherical particles near the onset of jamming to weak vibrations. Vibrations are added by displacing the packing along a single or a combination of eigenmodes of the dynamical matrix of the mechanically stable packing.  The frequency content of the vibrated system can be obtained from the Fourier transform of the particle displacements.  We first calculate and then confirm numerically the characteristic amplitude of the vibrations required to break the first interparticle contact in the packing as a function of overcompression Δϕ and system size N.  The characteristic amplitude at which the first interparticle contact breaks depends strongly on the frequency content of the initial perturbation and its subsequent evolution.   In addition, in overcompressed systems with m = > 0 contacts above the isostatic number, we measure the characteristic amplitude required to break m+1 interparticle contacts at which the system transitions from a solid-like to a liquid-like behavior.  Finally, we show preliminary studies of the thermal conductivity of the packings as a function of the amplitude and frequency content of the vibrations.  We find that the thermal conductivity is sensitive to the breaking and reforming of interparticle contacts.