Localized mesh refinement based on modified laplacian smoothing technique for finite element forging simulations

Abstract

It is well known that the quality and efficiency of the design of metal forming processes can be significantly improved with the aid of effective numerical simulations. However, one of the prominent features in the metal forming analysis using the finite element method is that the initial simple workpiece geometry becomes severely distorted by material flow, causing mesh degeneration due to locally concentrated deformation. Thus, an effective remeshing scheme is needed to continue the analysis and obtain more accurate analysis results. In the present investigation, a study on two-dimensional quadrilateral and three-dimensional hexahedral remeshing was carried out for two- and three-dimensional metal forming analyses, respectively. In the field of two-dimensional metal forming simulations, one of the most important issues is the improvement of solution accuracy and computational efficiency accompanied with automation of analyses. Thus, the present study on two-dimensional remeshing focused on the development of adaptive quadrilateral remeshing schemes and implementation of a robust remeshing program for full automation of simulations. For this, studies on the specification of mesh density and automatic quadrilateral mesh generation were carried out. In particular, new algorithms for the specification of mesh density according to the distribution of effective strain-rate gradients and the smoothing of such mesh density conditions using fast Fourier transform (FFT) and low-pass filtering techniques were proposed. Also, a coarsening function and modified Laplacian smoothing technique for repositioning of nodes during the mesh generation process were proposed. In order to evaluate the effectiveness of each procedure during the whole remeshing process, effects of each scheme were investigated for reference to actual remeshing examples. Finally, analyses of ring gear forging, flat die extrusion, and pin shape multi-stage forging were carried out to investigate the ef...