Gradient-based refinement indicators in adaptive finite element analysis with special reference to sheet metal forming

Two mesh refinement indicators based on the gradients of effective stress ( GSIG) and effective plastic strain (GEPS), respectively, are proposed for a daptive finite element analysis of the large deformation quasi-static or dy namic response of shell structures. The mesh refinement indicators are base d on equi-distributing the variation of stresses or plastic strains over th e elements of the mesh. A program module is developed and implemented in th e non-linear explicit finite element code LS-DYNA. This module provides ele ment-wise refinement evaluations so that selective mesh refinements are car ried 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 pr ocess is used as a numerical model, including both material and geometrical non-linearities, in order to demonstrate the versatility of the two refine ment indicators. Four different refinement indicators, based on, angle chan ge, thickness change, GSIG and GEPS, are applied in this investigation. The numerical results are compared with experimental results regarding the thi ckness distribution versus cup height, cup height variation versus circumfe rence angle, effective plastic strain in the deformed skeet and punch force . It is shown that the proposed indicators can identity finite elements whi ch have high gradients of effective stress or effective plastic strain so t hat the mesh is refined in the regions undergoing the most severe deformati ons and the numerical results are improved.