A fast detection algorithm based on the envelope function of dilated polyhedron

Abstract

The dilated polyhedron is generated by the Minkowski Sum with a basic polyhedron and a dilated sphere. It has characteristics of both polyhedron and sphere and can be employed for the discrete element simulation of complex shaped particles. The weighted summation of the sphere function and the second-order dilated function of polyhedron is adopted as the envelope function of the dilated polyhedron. The contact detection problem of dilated polyhedrons is translated into an optimization problem between two envelope functions, which improves the detection efficiency of dilated polyhedrons. The contact center between these two envelope functions can be obtained through the optimization problem which can be solved by the Lagrange multiplier method. Based on the contact center, the nearest points on each basic polyhedron can be detected quickly, and therefore the contact normal and overlap between these two particles can be solved accordingly. With the above method, an improvement in the contact detection of dilated polyhedra is achieved by avoiding the complexity that caused by the calculation of each geometric feature in early methods. This article develops a non-spherical DEM based on the dilated polyhedron with the fast contact detection algorithm and the nonlinear contact force model. The single-particle falling process is simulated to analyze the effect of the smoothness parameter to the result. The analysis illustrates that the smoothness parameter has small effect at the range of 0.0001–0.1. Besides, the smaller the smoothness parameter is the closer the results, which shows that the method of this article has good stability. The discharge process of multiple particles in the rectangle hopper with different particle shapes is simulated, while the residual particle fraction during hopper discharge is adopted to validate with existing experimental and numerical results. The reliability of the fast detection algorithm and the nonlinear contact model proposed in this paper is verified by the validation.