A stabilized formulation with maximum entropy meshfree approximants for viscoplastic flow simulation in metal forming

Abstract

The finite element method is the reference technique in the simulation of metal forming and provides excellent results with both Eulerian and Lagrangian implementations. The latter approach is more natural and direct but the large deformations involved in such processes require remeshing-rezoning algorithms that increase the computational times and reduce the quality of the results. Meshfree methods can better handle large deformations and have shown encouraging results. However, viscoplastic flows are nearly incompressible, which poses a challenge to meshfree methods. In this paper we propose a simple model of viscoplasticity, where both the pressure and velocity fields are discretized with maximum entropy approximants. The inf-sup condition is circumvented with a numerically consistent stabilized formulation that involves the gradient of the pressure. The performance of the method is studied in some benchmark problems including metal forming and orthogonal cutting.

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Acknowledgments

Francesco Greco acknowledges the travel research fellowship awarded by the Fondo Sociale Europeo. Marino Arroyo and Christian Peco acknowledge the support of the European Research Council under the European Community’s 7th Framework Programme (FP7/2007-2013)/ERC grant agreement nr 240487, and of the Ministerio de Ciencia e Innovacion (DPI2011-26589). MA acknowledges the support received through the prize “ICREA Academia” for excellence in research, funded by the Generalitat de Catalunya. CP acknowledges FPI-UPC Grant and FPU Ph.D. Grant (Ministry of Science and Innovation, Spain).

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Greco, F., Filice, L., Peco, C. et al. A stabilized formulation with maximum entropy meshfree approximants for viscoplastic flow simulation in metal forming. Int J Mater Form 8, 341–353 (2015). https://doi.org/10.1007/s12289-014-1167-x

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Keywords

  • Maximum entropy
  • Metal forming
  • Viscoplasticity
  • Stabilization