Investigation of time integration schemes for finite element analysis of metal forming processes

Abstract

In the fmite element simulation of metal forming processes the sources of errors that lead to volume change were studied. The study revealed that two major sources of error in volume change are the error in the velocity solution and the truncation error inherent in the updating scheme. Different methods for updating were implemented and simulation of experiments were carried out to compare with the experimental result. Effects of updating scheme on volume change and predicted loads were studied. The finite element formulation based on the penalty method leads to an excessive volume change if the penalty constant is not selected properly. A very large penalty constant leads to ill-condition of the stiffness matrix and the velocity solution does not converge. A simple method has been proposed to fmd an optimum value of the penalty constant that will ensure convergence of the velocity solution and effectively impose the incompressibility constraint.