14th World Congress on Computational Mechanics (WCCM) ECCOMAS Congress 2020) Virtual Congress: 11-15 January 2021 F. Chinesta, R. Abgrall, O. Allix and M. Kaliske (Eds) APPLICATIONS OF A NODAL-INTEGRATION-BASED FINITE ELEMENT METHOD TO NON-LINEAR PROBLEMS Yabo.Jia 1 , Jean-Baptiste.Leblond 2 , Jean-Christophe.Roux 1 , Remi.Lacroix 3 and Jean-Michel.Bergheau 1 1 University of Lyon, ENISE, LTDS, CNRS, UMR 5513. 58 rue Jean Parot, 42023 Saint-Etienne Cedex 02, France, yabo.jia@enise.fr, jean-christophe.roux@enise.fr, jean-michel.bergheau@enise.fr 2 University of Sorbonne, Institut Jean Le Rond dAlembert, CNRS, UMR7190 4 place Jussieu, 75005 Paris, France jbl@lmm.jussieu.fr 3 ESI FRANCE, batiment Le Rcamier, 70 rue Robert, 69006 Lyon, France Key words: Nodal integration technique, Tetrahedral meshes, Numerical simulation, Bending, Elasto- plasticity, volumetric locking, Thermo-mechanical simulation Abstract. In this paper, we firstly introduce a nodal-integration-based finite element method. The method allows the use of first-order tetrahedral elements without suffering from the volumetric lock- ing problem. The most important advantage of tetrahedral meshes is that they can be automatically generated for complex geometries using existing reliable meshing tools. The method is then applied to 3 types of applications. The first application is a large displacement, large strains elastic-plastic simu- lation on a notched specimen. The second application is an elastic-plastic bending problem. And the last example concerns the numerical simulation of the thermo-mechanical problem. In all the cases, the solution given by the nodal-integration-based FEM is compared to more classical FEM results. 1 INTRODUCTION Finite element simulations of the behavior of structures made up of materials obeying the von Mises plasticity criterion (the most commonly used criterion especially for metal materials) face particular difficulties. These difficulties come from the plastic incompressibility condition imposed by the behavior of the material. This condition of (nearly-)incompressibility which should be resolved at each integration point can lead to a volumetric locking phenomenon. Finite element formulations have thus been proposed to alleviate these difficulties. These formulations are generally based either on reduced numerical integration schemes, or on mixed formulations of the problem [1, 2]. In practice, formulations based on reduced integration schemes are easily applicable only with hexahedral elements. The absence of automatic meshing tools with this type of finite element then leads engineers to tedious operations which are costly in human time. The existence of automatic tetrahedral meshing tools gives this type of finite element an indisputable economic advantage. New 1