Global and local mechanical responses for necking of rectangular bars using Updated and Total Lagrangian finite element formulations

Abstract

In simulations of forged and stamping processes using the finite element method, load displacement paths and three-dimensionalstress and strains states should be well and reliably represented. The simple tension test is a suitable and economical tool to calibrateconstitutive equations with finite strains and plasticity for those simulations. A complex three-dimensional stress and strain statesare developed when this test is done on rectangular bars and the necking phenomenon appears. In this work, global and localnumerical results of the mechanical response of rectangular bars subjected to simple tension test obtained from two different finiteelement formulations are compared and discussed. To this end, Updated and Total Lagrangian formulations are used in order to getthe three-dimensional stress and strain states. Geometric changes together with strain and stress distributions at the cross sectionwhere necking occurs are assessed. In particular, a detailed analysis of the effective plastic strain, stress components in axial andtransverse directions and pressure, and deviatoric stress components is presented. Specific numerical results are also validated withexperimental measurements comparing, in turn, the performance of the two numerical approaches used in this study.