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Mathematical Problems in Engineering
Volume 2016, Article ID 1729638, 12 pages
Research Article

Global and Local Mechanical Responses for Necking of Rectangular Bars Using Updated and Total Lagrangian Finite Element Formulations

1Facultad de Ingeniería e ITIC, Universidad Nacional de Cuyo, Centro Universitario, Parque Gral. San Martín, 5500 Mendoza, Argentina
2Departamento de Ingeniería Mecánica y Metalúrgica, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, 7820436 Santiago, Chile

Received 24 January 2016; Revised 20 June 2016; Accepted 21 June 2016

Academic Editor: John D. Clayton

Copyright © 2016 Claudio A. Careglio et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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