Research Of The Contact Algorithms For Discrete Element Method Based On Supershape Surface Model

Discrete element method is the most effective numerical methods to analyze and studythe issues related to particle matters currently, which has an important role in the developmentof mechanical, civil engineering and other related discipline. In the discrete element method,each particle is simulated by discrete element model, and therefore the similarity of discreteelement and particle shape largely determines the accuracy of the numerical simulation.Currently although the discrete element model has been developed a lot, mostly sphericaldiscrete element model is used, which cannot represent the irregular shapes accurately. Forthis limitation, this paper uses supershape surfaces as discrete element model to improve theaccuracy of simulation of particle shape, and study discrete element contact algorithm on thebasis of this model.Firstly, do analysis of discrete element model using to model complex shapes of theparticles. Use supershape surfaces to build discrete elemente model of irregular shape of theparticles, use mathematical method to express the space motion of discrete element model anduse the Euler angles to optimize the rotation of discrete element model.Secondly, on the basis of supershape discrete element model, study the discrete elementcontact detection algorithm by dividing into pre-contact detection and precise contactdetection. In the pre-contact detection, establish a spherical bounding box for supershapediscrete element model, and then use the bounding box technology to remove the particle thatcannot be contacted. In the precise contact detection, convert contact detection into anoptimization problem by the interior point approach, and then solve the interior point byNewton iteration method. Determine the contact state by calculate the geometric potentialfunction value in the interior point, and then solve the contact overlap (shortest distance) bythe distance of interior points.Finally, use the mix of C++and Matlab programming to program the discrete elementcontact algorithm based on the supershape surface, and give some examples to test thealgorithm, in order to confirm the feasibility and validity of the model and algorithm. Dosome analyses of the affection of the supershape shape parameter to computational efficiency, and the results show that the accuracy of the algorithm is high, but still the computationalefficiency of the algorithm need to be improved.The work of this paper overcome a certain extent the current limitations on the shape ofdiscrete element model, provide a new method for simulation of complex particles matter,have a certain significance for the development of the theory of discrete element method.