Girkmann problem with a Discrete Element Method

Cells of Voronoï are used as particles in the Discrete Element code CeaMka3D. This type of meshing does not leave geometrical space like that can be the case with spherical particles. This method has already been used successfully to simulate the propagation of seismic waves in a linear elastic medium in 2D or in 3D. In this paper, a specific axisymmetric formulation is presented. In a first part, the calculation of the volumetric deformation of a particle and the forces between particles are described. In a second part, the specific forces for the axisymmetric formulation are described. At last, this formulation is tested for the Girkmann problem. This axisymmetric benchmark has been presented in January 2008 by the International Association of Computational Mechanics (IACM) in order to test the singularity at the junction between shell and beam. The accuracy of the axisymmetric formulation for this Discrete Element Method is evaluated by this benchmark. The results of this Discrete Element Method are compared with others numerical methods.