Abstract
In this article, the formulation of hybrid type three dimensional rigid finite element method based on the second cone programming with the yield function of Drucker-Prager model is presented. As a spatial discretization, the classical four-node tetrahedral (C3D4) element is used for a velocity field and a facet based constant stress field is employed. To avoid instability in numerical calculations due to the semi-positive definiteness of the second invariant of a deviatoric stress tensor J2, a stabilization term based on the eigenvector of zero eigenvalue is added. Three examples are solved with the proposed method. It is found that the stabilization term is effective, and the importance of spatial discretization around highly sheared areas is confirmed. The proposed method provides over-estimated results, especially for the cases of higher internal friction angles. This discrepancy is perhaps due to the deformation constraints of C3D4 elements.
