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Stress calculations for assemblies of inelastic speres in uniform shear

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Summary

Previous work on assemblies of inelastic, frictional disks is extended to three dimensions in a molecular-dynamics study of steady shearing flow of an idealized granular material consisting of equal-sized spherical particles that are smooth but inelastic. Cumulative time and space averages are calculated for several diagnostic quantities including the kinetic and potential energy densities, the R.M.S. (deviatoric) velocity and both the kinetic and potential contributions to each component of the stress tensor. Under steady-state shearing deformation the kinetic-energy-density (granular temperature) generally is found to increase as the solids fraction is decreased and decrease as the binary-collision coefficient-of-restitution is decreased. For constant coefficient-of-restitution interactions the calculated stresses increase generally with the square of the strain rate, with exceptional behavior noted at extremes in solids loadings. The general trends of the calculated stresses and velocities are in substantial agreement with the Lun et al. linearized perturbation of Chapman-Enskog theory for slightly inelastic spheres. However, some significant differences are noted at very low (ν<0.1) and very high (ν>0.5) solids fractions. A variable coefficient-of-restitution interaction interaction model (decreasing as the impact velocity increases) results in calculated stresses that deviate from the constant coefficient-of-restitution behavior in a manner similar to that predicted by Lun and Savage. The calculated stresses are in rough agreement with experimental measurements; however, the calculated shear-stress to normal-stress ratio for spheres with coefficients of restitution between 0.8 and 0.95 are significantly below experimentally measured values for glass and polystyrene beads in annular shear cell tests. Based on effects seen in two-dimensional calculations, the inclusion of interparticulate friction and particle rotations are expected to significantly reduce the discrepancy.

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Authors and Affiliations

  1. Lawrence Livermore National Laboratory, 94550, Livermore, CA, USA

    O. R. Walton & R. L. Braun

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  1. O. R. Walton
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  2. R. L. Braun
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With 6 Figures

Work performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under Contract W-7405-Eng-48.

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Walton, O.R., Braun, R.L. Stress calculations for assemblies of inelastic speres in uniform shear. Acta Mechanica 63, 73–86 (1986). https://doi.org/10.1007/BF01182541

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  • DOI: https://doi.org/10.1007/BF01182541

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