Determination of Yield Surfaces for Isotropic Non-Cohesive Particulate Materials by the Discrete Element Method

We perform numerical simulations using the discrete element method (DEM) to determine yield surfaces for large samples of randomly packed uniform spheres with constant normal and tangential contact stiffnesses (linear spring model) and uniform inter-particle friction coefficient μ, for a large range of values of the inter-particle friction coefficient μ. The beauty of DEM is that the micromechanical properties of the spheres, especially the inter-particle friction coefficient μ, are known exactly. Further, simulations can be performed with particle rotation either prohibited or unrestrained, which provides an effective means for evaluating analytical models that employ these assumptions. We compare the resulting yield surfaces to the Mohr–Coulomb, Matsuoka–Nakai, Lade–Duncan, and Drucker–Prager yield surfaces, and determine the relationship between the resulting material friction angle ϕ on the macroscale and the inter-particle friction coefficient μ (or the inter-particle friction angle ϕ _μ ) on the microscale. We find the Lade–Duncan yield surface provides the best agreement, by far, with the simulations in all cases. We also monitor inter-particle friction work and particle rotation within each specimen during the DEM simulations, both globally and on a particle-by-particle basis, and we compare the results obtained from DEM simulations in which the spheres were allowed full three-dimensional translational and rotational freedom of motion and DEM simulations in which particle rotation was prohibited.