Stress fluctuations in continuously sheared dense granular materials Piroz Zamankhan and Tero Tynja ¨ la ¨ Department of Energy Technology, Lappeenranta University of Technology, Fin-53851, Lappeenranta, Finland William Polashenski, Jr. Lomic, Inc., 200 Innovation Boulevard, State College, Pennsylvania 16803 Parsa Zamankhan and Pertti Sarkomaa Department of Energy Technology, Lappeenranta University of Technology, Fin-53851, Lappeenranta, Finland ~Received 9 March 1999! At high solid concentrations, computer simulations of sheared granular materials comprised of randomly arranged, monodisperse, smooth, inelastic spherical particles flowing in a Couette geometry show large fluc- tuations in the normal stress at the walls. These fluctuations are characterized by a marked asymmetric amplitude distribution similar to those observed in recent experiments. In these systems the particles’ mean square displacement in the shear direction is observed to vanish locally which indicates the formation of crystallized regions. However, there are other regions in the system with nonzero values for the mean square displacement in the shear direction. This observation indicates that a sheared monodisperse granular material initially in a disordered state could evolve to a system in which the crystal phase is formed largely with a well-defined interface between different phases. The periodic phase transition is observed between the com- pressed, highly ordered crystalline state and the dilated, less ordered state of the layer of particles adjacent to the wall, which may explain the stick-slip behavior which occurred in the experiments. @S1063-651X~99!05612-3# PACS number~s!: 45.70.Mg, 61.20.Ja, 83.50.2v I. INTRODUCTION The interest in granular flows, such as grain flow in silos @1#, catalytic particle flow in beds @2#, rockfalls @3#, and pack-ice flows @4#, arises because granular flows exhibit a wide range of rheological behavior related to the kinds of interactions that take place between grains. It appears that many real engineering problems, such as applications to the industrial handling, are in a flow regime involving instanta- neous collisions between the grains as well as long lived sliding contacts @5#. In contrast, there is clear experimental evidence @6# that the dynamics of grains may be dominated by collisions rather than sliding contacts even in slow dense flows. Therefore, the physical relevance of the assumption that grains in a dense flow have complex interactions of fi- nite duration @7# remains a topic of controversy. The motivation for this study is, therefore, to examine carefully the importance of particle surface roughness in de- scribing the observed dynamical features of continuously sheared granular materials at high solid concentrations @8#. To this end, computer simulations based on the model de- scribed in Sec. II are used to produce results suitable for comparison with available experimental data. Simulations of shearing flows of randomly arranged, monodisperse, spheri- cal particles with rough or smooth surfaces were carried out in a Couette geometry. The results of simulations are pre- sented in Sec. III. The time series of the dimensionless nor- mal stress at the walls revealed the presence of stick-slip dynamics in the shearing flows of a system comprised of smooth particles at solid volume fraction of 0.6, where a crystalline phase is formed which spans a large part of the computational box. The present results are of interest since they may motivate new theoretical efforts toward under- standing the microscopic origin of stick-slip behavior. II. SIMULATION MODEL One possible method for the simulation of granular as- semblies under shear is the soft sphere molecular dynamics approach in which each particle during a collision interacts with its neighbors by a damped normal force, which is a function of the degree of deformation at points of contact, as well as a superimposed shear force, which is simply related to the normal force by introducing a coefficient friction m @9#. In this time-driven simulation, to assure sufficient accu- racy, the interaction force between the particles must be cal- culated at least 100 times due to the presence of a very large gradient of the interaction force during a collision. There- fore, a three-dimensional simulation with a large number of particles may not currently be achievable using this ap- proach. It has been assumed previously that an event-driven simu- lation algorithm can be used for the simulation of a dense granular flow in which the effect of friction may be of inter- est @10#. The algorithm allows the creation of the trajectories of a large number of particles in the simulation box by cal- culating only the precollisional and postcollisional velocities and spins, without considering the details of the collision. Given that previous models @10,11# do not provide the details of the collisions, an obvious question is how could these types of models be used to study the frictional effects. To address this question, a brief discussion of the present model is given below. In the present study, the hard-sphere model of Alder and PHYSICAL REVIEW E DECEMBER 1999 VOLUME 60, NUMBER 6 PRE 60 1063-651X/99/60~6!/7149~8!/$15.00 7149 © 1999 The American Physical Society