Author: Fangtao Yang

Publisher:

Published: 2017

Total Pages: 0

ISBN-13:

This work is part of the research carried out in the framework of a collaboration between the Roberval laboratory of the Compiègne University of Technology and the team within the framework of the project ANR-14-CE07-0035 LASMIS of the Charles Delaunay Institute of Technology University of Troyes. In this work, we present a three-dimensional adaptive Pi-methodology of finite elements to represent the initiation and propagation of cracks in ductile materials. An elastoplastic model coupled with the isotropic damage proposed by the LASMIS / UTT team is used. The targeted applications will mainly concern the metal forming. In this context, an updated Lagrangian formulation is used and frequent remeshing is essential in order to avoid the strong distortion of elements due to large plastic deformations and to follow the modifications of the topology resulting in the creation of cracks. The size of the new mesh must allow at a lower cost to accurately represent the evolution of the gradients of the physical quantities representative of the studied phenomena (plasticity, damage ...). We propose empirical indicators of size of elements based on the plastic deformation as well as on the damage. A piecewise defined curve represents the evolution of the element size according to the severity of the plasticity and, if appropriate, the damage. The cracks are represented by a method of destruction of elements which allows an easy description of the geometry and a simplified treatment of the cracking without any need for additional criteria. On the other hand, to allow a realistic description of the cracks, the latter must be represented by erosion smaller elements. An ABAQUS / Explicit@ solver is used with quadratic tetrahedral elements (C3DIOM), avoiding in particular the problems of numerical locking occurring during the analysis of structures in compressible or quasi-incompressible material. The control of the smaller mesh size is important in an explicit context. In addition, for softening phenomena, the solution depends on the mesh size considered as an intrinsic parameter. A study has shown that when the mesh is sufficiently refined, the effects of mesh dependence are reduced. In the literature, the costs of frequent meshing or remeshing are often considered prohibitive and many authors rely on this argument to introduce, with success, alternative methods that limit the cost of remeshing operations without eliminating them ( XFEM for example). Our work shows that the cost of local remeshing is negligible compared to the calculation. Given the complexity of the geometry and the need to refine the mesh, the only alternative to date is to use a mesh in tetrahedra. The strategy of local remeshing tetrahedron is based on a bisection method followed if necessary by a local optimization of the grid proposed by A. Rassineux in 2003. The remeshing, even local, must be accompanied by field transfer procedures on both nodal variables and integration points. Node variables are, as most authors do, transferred using finite element shape functions. The 3D field transfer at Gauss points and the many underlying problems have been relatively untouched in the literature. The main difficulties to be solved in order to ensure the "quality" of the transfer concern the limitation of numerical diffusion, the lack of information near borders, the respect of boundary conditions, the equilibrium, the calculation costs, the filtering of the information points, crucial problems in 3D where the number of Gauss points used is several hundred. We propose a so-called "hybrid" method which consists, initially, in extrapolating the data at the Gauss points, in the nodes by diffuse interpolation and then in using the finite element form functions to obtain the value at the point considered.