Keywords: adaptive remeshing, forming process, geometrical and physical error estimator, thin sheet.

During the numerical simulation of forming processes (stamping, forging, bulging, etc..), the large plastic deformations imply large element distortion of initial mesh. It is then necessary to frequently remesh the part in order to be able to carry out the simulation and, in particular, to capture the geometrical details of surfaces under contact with forming tools. This remeshing procedure must be automatic and robust. Several remeshing methods have been proposed during the last years. The remeshing techniques presented in References [1,2,3,4,5] are based on the computation of a size map to govern a global remeshing of the part at each iteration. This kind of approaches needs the knowledge of the geometry of forming tools. Cho and Yang [6] have proposed a refinement algorithm which consists in splitting each deformed element in two elements along an edge. This procedure drags to the creation of small edges and consequently degenerates elements during repetitive refinement iterations.

This paper presents a new remeshing technique for the numerical simulation of thin sheet metal forming processes in three dimensions. The simulation of the forming process is based on an iterative process. At first, a coarse initial mesh of the part is generated with triangular or quadrilateral elements. At each iteration, a finite element computation is then realized in order to simulate numerically the forming process for a small displacement of forming tools. Remeshing is applied after each deformation increment. The proposed remeshing method is based on refinement and coarsening procedures. It is constituted by two steps using geometrical and physical criteria. It is given by the following scheme:

First step (geometrical criteria):

• coarsening procedure applied to elements which are in flat area,
• iterative refinement to restore mesh conformity,
• refinement procedure applied to elements which are in curved area (the refinement is applied in the vicinity of nodes for which the shape of the surface is changed and only if the minimal element size is not reached),
• iterative refinement to restore mesh conformity,

Second step (physical criteria):
While the mesh of the part does not conform to the physical size map:

• refinement procedure by using the physical criterion (refinement of the mesh element size with respect to the damage),
• iterative refinement to restore mesh conformity.

This process (simulation of the forming process for a small displacement step of forming tools, remeshing of the part) is repeated until the final tool displacement is reached. Thanks to this remeshing procedure, the mechanical fields are simply induced from the old mesh into the new mesh.

One of the major advantage of our approach is that the remeshing is applied without the knowledge of the forming tools under contact with the part. The remeshing technique has been implemented with triangular and quadrilateral elements in the ABAQUS solver. Some application examples are presented in order to show the efficiency of our remeshing technique.

1

O.C. Zienkiewicz and J.Z. Zhu, "Adaptivity and mesh generation", in Int. J. Numer. Methods Eng. 32, 783-810, 1991. doi:10.1002/nme.1620320409

2

L. Fourment and J.-L. Chenot, "Adaptive remeshing and error control for forming processes". Revue européenne des éléments finis 3, 2, 247-279, 1994.

3

P. Coorevits, J.-P. Dumeau and J.-P. Pelle, "Analyses éléments finis adaptatives pour les structure tridimensionnelles en élasticité". Revue européenne des éléments finis 5, 3, 341-373, 1996.

4

T.Coupez, "Génération de maillage et adaptation de maillage par optimisation locale". Revue européenne des éléments finis 9, 4, 403-422, 2000.

5

H. Borouchaki, A. Cherouat, P. Laug and K. Saanouni, "Adaptive remeshing for ductile fracture prediction in metal forming". C.R. Mecanique 330, 709-716, 2002. doi:10.1016/S1631-0721(02)01519-X

6

J.-W. Cho and D.-Y. Yang, "A mesh refinement scheme for sheet metal forming analysis". Proc. of the 5th International Conference, NUMISHEET'02, 307-312, 2002.

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