Criteria for static equilibrium in particulate mechanics computations

The underlying physics of granular matter can be clearly solved using particulate mechanics methods, e.g. the discrete element method (DEM) that is inherently discontinuous and heterogeneous. To solve static problems, explicit schemes using dynamic relaxation procedures have been widely employed, in which naturally dynamic material parameters are typically adapted into pure numerical artifacts with the sole purpose of attaining meaningful results. In discrete computations using these explicit schemes, algorithmic calibration is demanded under general conditions in order to achieve quasi‐static states. Until now, procedures for algorithmic calibration have remained rather heuristic. This paper presents two criteria, using the concept of homogenized stresses, for evaluating equilibrium in quasi‐static applications of particulate mechanics methods. It is shown, by way of numerical examples, that the criteria for static equilibrium can be applied successfully to obtain quasi‐static solutions in explicit DEM codes through algorithmic calibrations. A general procedure is proposed herein for carrying out the algorithmic calibration effectively and efficiently.