Application of three-node triangular element with drilling and strain degrees of freedoms to rigid plastic finite element method and verification of its validity

Abstract

The rigid plastic finite element method (RPFEM) is used in many re-meshing procedures in material processing analysis. Currently, the four-node quadrilateral element, which can avoid volumetric locking, is applied in the RPFEM. However, it is desirable to apply the three-node triangular element instead because of its easy and robust mesh generation procedure. This study applied the three-node triangular element with drilling and strain degrees of freedoms (GNTri3) to the RPFEM, the validity of which was verified by analyzing some numerical examples. First, as verification for the volumetric locking characteristic of the GNTri3, FEM analysis of a nearly incompressible elastic body under plane strain conditions was performed. Volumetric locking was recognized by applying full integration to the element stiffness matrix of the GNTri3. Therefore, it was revealed that the RPFEM using the GNTri3 is necessary for applying selective reduced integration to the element stiffness matrix. Analysis of the RPFEM using the GNTri3 showed that the tool pressure was in good agreement with theoretical solutions and FEM results obtained using a conventional four-node quadrilateral element at a rigid punch indentation. In addition, reasonable material processing deformations were computed in the plane strain compression test. Therefore, validity of the RPFEM using the GNTri3 was verified by numerical results.