ADAPTIVE FINITE ELEMENT SIMULATION OF SHEET METAL FORMING PROCESSES USING GRADIENT BASED INDICATORS

Two mesh refinement indicators based on the gradients of effective stresses (GSIG) and effective plastic strains (GEPS), respectively, are proposed for adaptive finite element analysis of the large deformation, quasi-static or dynamic response of shell structures. The mesh refinement indicators are based on equi-distributing the variation of stresses or plastic strains over the elements of the mesh. A program module is developed and implemented in the nonlinear explicit finite element code LS-DYNA. This module provides element-wise refinement evaluations so that selective mesh refinements are carried out in regions of the mesh where the values of local indicators exceed a user-specified tolerance. The FE model of a conventional deep drawing process is used as numerical model, including both material and geometrical nonlinearities, in order to demonstrate the versatility of the two refinement indicators. Four different refinement indicators, based on angle change, thickness change, GSIG and GEPS based are applied in this investigation. To verify the numerical results against experiments, the anisotropic low carbon steel, FEP04, is used as a reference material. The numerical results are compared with experimental results regarding the thickness distribution versus cup height, effective plastic strain in the deformed sheet and punch force. It is shown that the new proposed indicators can identify finite elements, which have high gradients of stresses or strains so that the mesh is refined in the regions undergoing the most severe deformations and the numerical results are improved.