Unjamming of granular packings due to local perturbations: Stability and decay of displacements

Abstract

We study the mechanical response generated by local deformations in jammed packings of rigid disks. Based on discrete element simulations we determine the critical force of the local perturbation that is needed to break the mechanical equilibrium and examine the generated displacement field. Displacements decay as a power law of the distance from the perturbation point. The decay exponent and the critical force exhibit nontrivial dependence on the friction: Both quantities are nonmonotonic and have a sharp maximum at the friction coefficient 0.1. We find that the mechanical response properties are closely related to the problem of force-indeterminacy where similar nonmonotonic behavior was observed previously. We establish direct connection between the critical force and the ensemble of static force networks.

Numerical analysis of compression mechanics of highly polydisperse granular mixtures with different PSD-s

“…This inconsistency may be due to the fact that the structural properties of granular packing and its mechanical behavior depend on both, the particle size polydispersity and the contact density [25][26][27]. Because the contact density is determined via a generation procedure and loading process, the order of the curves for different distributions as well as their trends may differ among various projects.…”

Unjamming due to local perturbations in granular packings with and without gravity

“…We checked that for small gap sizes the displacement field (up to a constant factor) and the critical force become independent of the size of the gap. Our numerical measurements are performed in this gap-independent region; the size of the gap ξ is set to 10 −9 [15]. This value is far larger than the displacement scale 10 −14 that arises from the noise level of particle velocities.…”

“…1(a)]. As this case has been described in [15], here only a short review is given. At the perturbation point we enforce the contacting surfaces to open up to a small gap and determine the force that is needed to fulfill this constraint (critical force).…”

“…1(a)]. This part is the full exposition and expansion of the results presented and considered from another point of view in [15]. Then we study more realistic packings that are settled under gravity [ Fig.…”

“…Our systems are two-dimensional disordered packings of disks. First, we test ideal homogeneous packings prepared by an isotropic external pressure and with fully periodic boundary conditions [15,16] [ Fig. 1(a)].…”