We report on a numerical study of the shear flow of a simple two-dimensional model of a granular material under controlled normal stress between two parallel smooth, frictional walls, moving with opposite velocities ±V . Discrete simulations, which are carried out with the contact dynamics method in dense assemblies of disks, reveal that, unlike rough walls made of strands of particles, smooth ones can lead to shear strain localization in the boundary layer. Specifically, we observe, for decreasing V , first a fluid-like regime (A), in which the whole granular layer is sheared, with a homogeneous strain rate except near the walls; then (B) a symmetric velocity profile with a solid block in the middle and strain localized near the walls and finally (C) a state with broken symmetry in which the shear rate is confined to one boundary layer, while the bulk of the material moves together with the opposite wall. Both transitions are independent of system size and occur for specific values of V . Transient times are discussed. We show that the first transition, between regimes A and B, can be deduced from constitutive laws identified for the bulk material and the boundary layer, while the second one could be associated with an instability in the behavior of the boundary layer. The boundary zone constitutive law, however, is observed to depend on the state of the bulk material nearby.

The role of rotational degrees of freedom and of microscopic contact properties at smooth walls in two dimensional planar shear has been investigated by contact dynamics simulations of round hard frictional particles. Our default system setup consists of smooth frictional walls, giving rise to slip. We show that there exists a critical microscopic friction coefficient at the walls, above which they are able to shear the granular medium. We observe distinctive features at this critical point, which to our knowledge have not been reported before. Activating rolling friction at smooth walls reduces slip, leading to similar shear behavior as for rough walls (with particles glued on their surface). Our simulations with rough walls are in agreement with previous results, provided the roughness is strong enough. In the limit of small roughness amplitude, however, the distinctive features of shearing with smooth walls are confirmed.

A fully parallel version of the Contact Dynamics (CD) method is presented in this paper. For large enough systems, 100% efficiency has been demonstrated for up to 256 processors using a hierarchical domain decomposition with dynamic load balancing. The iterative scheme to calculate the contact forces is left domain-wise sequential, with data exchange after each iteration step, which ensures its stability. The number of additional iterations required for convergence by the partially parallel updates at the domain boundaries becomes negligible with increasing number of particles, which allows for an effective parallelization. Compared to the sequential implementation, we found no influence of the parallelization on simulation results. decomposition leads to causality problems. The algorithm presented in [15] conserves causality by reverting to an older state when violated. The best efficiency reached so far is a speedup proportional to the square root of the number of processors [15].In contrast to ED, lasting contacts between rigid bodies are considered in the realm of (multi)-rigid-body dynamics. Common to all its realizations is the treatment of contact forces as constraint forces, preventing interpenetration and, to a certain extent in the case of frictional contacts, sliding. When applying the rigid body modelling to problems like e.g. robotics [16,17] or granular media [18,19,20,21], different algorithms can in principle be used. Approximations with respect to the constraint of dry Coulomb friction enable the usage of powerful standard techniques for linear complementary problems (LCP) [22]. Other algorithms keep the isotropic friction cone, using a solver based on a modified time stepping scheme leading to a cone complementary problem (CCP) for the simulation of frictional contact dynamics [23]. Other approximations, leading to fast frictional dynamics (FFD) [24], yield a computational cost being only linear in the number of contacts and thus allow for impressive system sizes in terms of the number of particles. For investigations of e.g. the stress field in granular media, these approximations are prohibitive, though, and thus the non-smooth contact dynamics method [7], or commonly just contact dynamics, is widely employed. We will sketch the principle of this iterative procedure in section 2.1. Parallelization of the FFD method is straightforward and efficient [25,26], on the other hand, the parallel version suffers also from the undesired approximations. The parallel implementation of the CCP algorithm by the use of the Graphics Processing Unit (GPU) for large-scale multibody dynamics simulations is presented in [27]. In the present work we investigate the impact of the parallelization on the numerical solution of the CD method going beyond [25,26,27].Providing a parallel CD code is motivated by the need for large-scale simulations of dense granular systems of hard particles. The computation time even scales as O(N 1+2/d ) with the number of particles in CD [8] (d is the dimension of the system), while it...

No abstract

The planar shearing of dense systems of bidisperse as well as polydisperse, non-cohesive, hard, round, dissipative and frictional particles is simulated in two and three dimensions using Contact Dynamics. The system is sheared by smooth, frictional walls at constant shear velocities, subject to a constant normal force. Depending on the shear velocity, the system behavior belongs to one of the three different regimes (from high to low shear velocities): a) a fluid like state with almost homogeneous shearing, b) a block like state with symmetric velocity profiles and fluidization only at the walls, c) a state of broken symmetry, where a block moves essentially with one wall while possessing a shear zone at the other. The two shear velocities separating theses regimes do not depend on the distance between the walls.