Extent of force indeterminacy in packings of frictional rigid disks.

Static packings of frictional rigid particles are investigated by means of discrete element simulations. We explore the ensemble of allowed force realizations in the space of contact forces for a given packing structure. We estimate the extent of force indeterminacy with different methods. The indeterminacy exhibits a nonmonotonic dependence on the interparticle friction coefficient. We verify directly that larger force indeterminacy is accompanied by a more robust behavior against local perturbations. We also investigate the local indeterminacy of individual contact forces. The probability distribution of local indeterminacy changes its shape depending on friction. We find that local indeterminacy tends to be larger on force chains for intermediate friction. This correlation disappears in the large friction limit.

Shear zone refraction and deflection in layered granular materials.

Refraction and deflection of shear zones in layered granular materials were studied experimentally and numerically. We show that (i) according to a recent theoretical prediction [T. Unger, Phys. Rev. Lett. 98, 018301 (2007)] shear zones refract in layered systems in analogy with light refraction, (ii) zone refraction obeys Snell's law known from geometric optics, and (iii) under natural pressure conditions (i.e., in the presence of gravity) the zone can also be deflected by the interface, so that the deformation of the high friction material is avoided.

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

We investigate the unjamming response of disordered packings of frictional hard disks with the help of computer simulations. First, we generate jammed configurations of the disks and then force them to move again by local perturbations. We study the spatial distribution of the stress and displacement response and find long range effects of the perturbation in both cases. We record the penetration depth of the displacements and the critical force that is needed to make the system yield. These quantities are tested in two types of systems: in ideal homogeneous packings in zero gravity and in packings settled under gravity. The penetration depth and the critical force are sensitive to the interparticle friction coefficient. Qualitatively, the same nonmonotonic friction dependence is found both with and without gravity, however the location of the extrema are at different friction values. We discuss the role of the connectivity of the contact network and of the pressure gradient in the unjamming response.

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

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 a 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 indeterminate where similar nonmonotonic behavior was observed previously. We establish a direct connection between the critical force and the ensemble of static force networks.

Refraction of shear zones in granular materials.

We study strain localization in slow shear flow focusing on layered granular materials. A heretofore unknown effect is presented here. We show that shear zones are refracted at material interfaces in analogy with refraction of light beams in optics. This phenomenon can be obtained as a consequence of a recent variational model of shear zones. The predictions of the model are tested and confirmed by 3D discrete element simulations. We found that shear zones follow Snell's law of light refraction.

Shear zones in granular media: three-dimensional contact dynamics simulation.

The properties of shear zones forming in slow three-dimensional granular flow are investigated. We simulate a straight version of the split-bottom shear cell. It is shown that the same type of wide shear zones is obtained in the presence as well as in the absence of gravity. We investigate the relaxation of the material toward stationary flow and analyze the stress and the velocity fields. A functional form of the widening of the shear zone inside the bulk is given. We discuss the growth of the region where the material is in the critical state. The growth of this critical zone turns out to be responsible for the initial transient of the shear zone.

Force indeterminacy in the jammed state of hard disks.

Granular packings of hard disks are investigated by means of contact dynamics which is an appropriate technique to explore the allowed force realizations in the space of contact forces. Configurations are generated for given friction coefficients, and then an ensemble of equilibrium forces is found for fixed contacts. We study the force fluctuations within this ensemble. In the limit of zero friction, the fluctuations vanish in accordance with the isostaticity of the packing. The magnitude of the fluctuations has a nonmonotonous friction dependence. The increase for small friction can be attributed to the opening of the angle of the Coulomb cone, while the decrease as friction increases is due to the reduction of connectivity of the contact network, leading to local, independent clusters of indeterminacy. We discuss the relevance of indeterminacy to packings of deformable particles and to the mechanical response properties.

Frictional coupling between sliding and spinning motion.

The tangential motion at the contact of two solid objects is studied. It consists of a sliding and a spinning degree of freedom (no rolling). We show that the friction force and torque are inherently coupled. As a simple test system, a sliding and spinning disk on a horizontal flat surface is considered. We calculate, and also measure, how the disk slows down and find that it always stops its sliding and spinning motion at the same moment. We discuss the impact of this coupling between friction force and torque on the physics of granular materials.