An element‐free Galerkin method for metal forming simulations

Abstract

Purpose

The purpose of this paper is to investigate the application of the element‐free Galerkin (EFG) method to the simulation of metal forming processes and to propose a strategy to deal with volumetric locking problem in this context.

Design/methodology/approach

The J₂ elastoplastic material model, employed in the work, assumes a multiplicative decomposition of the deformation gradient into an elastic and a plastic part and incorporates a non‐linear isotropic hardening response. The constitutive model is written in terms of the rotated Kirchhoff stress and the logarithmic strain measure. A Total Lagrangian formulation of the problem is considered in order to improve the computational performance of the proposed algorithm. The imposition of the essential boundary conditions and also of the unilateral contact with friction condition are made by the application of the Augmented Lagrangian method. Here, aspects related to the volumetric locking are investigated and an F‐bar approach is applied.

Findings

The results show that the proposed approach presents no volumetric locking phenomenon when using the mean dilation approach. Moreover, differently from finite element approximations, no hour‐glass instabilities in the deformation pattern are observed, avoiding in this way the need to devise additional stabilization procedures in the proposed procedure.

Originality/value

This paper demonstrates the implementation and validation of the mean dilation approach, in the scope of the EFG, which was successful in coping with the volumetric locking phenomena and presented no hour‐glass instabilities in the problem cases considered in this work.

Citation

Rossi, R., Krajnc Alves, M. and Al‐Qureshi, H.A. (2009), "An element‐free Galerkin method for metal forming simulations", Engineering Computations, Vol. 26 No. 4, pp. 327-346. https://doi.org/10.1108/02644400910959142