Adaptive multiple scale meshless simulation on springback analysis in sheet metal forming

Springback is one of the major considerations in the design of part shape, die geometry and processing parameters of sheet metal forming. In this study, an adaptive multiple scale meshless method is developed to predict the amount of springback, which occurs after unloading in sheet metal forming. A two-dimensional meshless continuum approach is applied to the bending deformation of plate/shell structures. The meshless method called reproducing kernel particle method (RKPM) is modified to develop the springback analysis algorithm using two scales. The effective strain is decomposed into two scales, high and low. The two scale decomposition is incorporated into non-linear elasto-plastic formulation to obtain high and low components of effective stresses. The high scale component of effective stress indicates the high stress gradient regions without posterior estimation. Enrichment nodes with a proper refinement scheme are inserted/deleted in those high stress regions to exactly calculate the stress distribution and thus accurately predict the amount of springback. The simulation results show that the algorithm can effectively locate the high stress gradient regions and can be utilized as an efficient indicator for the adaptive refinement technique for non-linear elasto-plastic deformation. The comparison of the amount of springback via the processing parameters between experiment, FEM (ABAQUS), meshless method and adaptive meshless method shows that the adaptive meshless solutions are the closest to experiment results. Crown Copyright (C) 2010 Published by Elsevier Ltd. All rights reserved.