NS-FEM/ES-FEM for contact problems in metal forming analysis

A new approach based on the node-based smoothed finite element method (NS-FEM) / edge-based smoothed finite element method (ES-FEM) is presented for the analysis of contact-impact problems with large deformations and for the simulation of metal forming processes. The formulations are based on 3-node triangular and linear interpolation functions. A simple but general contact searching algorithm is used to treat the contact interface and an algorithm for the contact force is presented. In the presented methods, the strain field is smoothed by means of gradient smoothing technique over smoothing domains constructed associated with nodes for NS-FEM and element edges for ES-FEM. In the total Lagrangian formulation the strain smoothing is performed for the deformation gradient and Green strain. The smoothed deformation gradient, smoothed strain tensor, and the smoothed stress tensor are derived at the reference (or initial) configuration. ES-FEM is used to analyze deviatoric part and NS-FEM is selectively employed in the volumetric part of deformation in order to relax the incompressible constraints and remedy the volumetric locking. Solutions to upsetting, extrusion of metals with large material distortions are given to show the effectiveness and efficiency of the proposed method.