Keywords: remeshing, finite element, field data remapping, optimization.

The present paper introduces a new remapping technique for the mechanical field when remeshing occurs during a finite element analysis of complex metal forming processes such as stamping or forging where the mesh element distortion occurs frequently. A remapping technique consists in transferring required mechanical fields associated with the old distorted mesh to the new mesh in order to restore the material state on the new mesh and continue the finite element analysis using the latter. In the first section of the paper, we present different remapping techniques that were developed during the last decades. The common objective of these techniques was to generate a field associated with the new mesh that fits well to the old field and satisfies mechanical equations verified by the old one without introducing excessive numerical diffusion. We can cite from these techniques, the variational technique [1], the SPR technique [2,3,4], the inverse isoparametric mapping technique [5,6] and the constrained or unconstrained optimization techniques that aims to minimize the gap between the mechanical field associated with the new mesh and that associated with the old one in a sense of a certain mathematical norm.

In the second section, we describe briefly the theoretical aspects of our remapping technique. The latter is an optimization based algorithm to minimize the norm of the committed finite element error between the mechanical field associated with the old mesh and that associated with the new one. The method distinguishes between the domain and its boundary in the minimization process and takes into account the field associated with them separately. This aims to more accurately determine the new field at the domain and its boundary and so well preserve the different mechanical properties verified by the old one. In recent works [7,8], the and mathematical norms of finite element error was used to define the minimization problem but in our approach these two norms are combined in order to benefit from their advantages together. So, the norm, when it is used, guarantees the similarity between the old and new fields and their derivatives and the norm guarantees, on its side, the similarity of the two fields at the whole domain or at its boundary when combined with the or the norm.

In the third section, we try to show the efficiency of the proposed transfer procedure through a numerical analysis of a tensile test using the remeshing technique. The simulation is based on an iterative process and the final deformation is obtained by a number of small increments of deformation. The material behavior is described by an elasto-plastic model coupled with the ductile damage [9]. At each iteration, a new mesh of the domain is defined and a set of nineteen internal variables (the stress components, the isotropic and kinematic hardening component and the ductile damage) is remapped. The displacement-force curves given by the different analysis performed using the different varieties of the remapping technique have shown that the minimization of the norm of error gives the best results in term of energy conservation. it was shown also that the remapping technique is directly influenced by the error estimators and the changes in topology of two successive mesh. Notice also that the major part of numerical diffusion in the remapping process is due to the used recovery technique. These different influence factors will be analyzed and presented in future works.

1

M. Ortiz and J.J. Quigley. "Adaptive mesh refinement in strain localization problems", Comp. Meth. App. Mech. Eng., (90):781-804, 1991. doi:10.1016/0045-7825(91)90184-8

2

O.C Zienkiewicz and J.Z. Zhu. "The superconvergent patch recovery and adaptive finite element refinement", Comp. Meth. App. Mech. Eng., 1992. doi:10.1016/0045-7825(92)90023-D

3

O.C Zienkiewicz and J.Z. Zhu. "The superconvergent patch recovery and a posteriori error estimates, part 1: The recovery technique", Int. J. Num. Meth. Eng., 1992. doi:10.1002/nme.1620330702

4

O.C Zienkiewicz and J.Z. Zhu. "The superconvergent patch recovery and a posteriori error estimates, part 2: Error estimates and adaptivity", Int. J. Num. Meth. Eng., 1992. doi:10.1002/nme.1620330703

5

N-S. Lee and K-J. Bathe. "Error indicator and adaptive remeshing in large deformation finite element analysis", Finite Elements in analysis and design, (16):99-139, 1994. doi:10.1016/0168-874X(94)90044-2

6

D. Peric, Ch. Hochard, M. Dutko, and D.R.J. Owen. "Transfer operators for evolving meshes in small strain elasto-plasticity", Comp. Meth. App. Mech. Eng., (137):331-344, 1996. doi:10.1016/S0045-7825(96)01070-5

7

M.M. Rashid. "Material state remapping in computational solid mechanics", Int. J. Num. Meth. Eng., (55):431-450, 2002. doi:10.1002/nme.508

8

Xiaoming Jiao and Michael T. Heath. "Common-refinement-based data transfer between non-matching meshes in multiphysics simulations", Int. J. Numer. Meth. Engng, (61):2402-2427, 2004. doi:10.1002/nme.1147

9

K. Saanouni, C. Forster, and F. Ben Hatira. "On the anelastic flow with damage", International Journal of Damage Mechanics, (3):141-169, 1994. doi:10.1177/105678959400300203

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