Incremental Volumetric Remapping Method: Analysis and Error Evaluation ...

Incremental Volumetric Remapping Method: Analysis and Error Evaluation

A.J. Baptista 1, J.L. Alves 2, M.C. Oliveira 1, D.M. Rodrigues 1, L.F. Menezes 1

1 CEMUC, University of Coimbra, Pólo II, Rua Luís Reis Santos, Pinhal de Marrocos, 3030-788 Coimbra, Portugal

2 Department of Mechanical Engineering, University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugal

Abstract. In this paper the error associated with the remapping problem is analyzed. A range of numerical results that assess the performance of three different remapping strategies, applied to FE meshes that typically are used in sheet metal forming simulation, are evaluated. One of the selected strategies is the previously presented Incremental Volumetric Remapping method (IVR), which was implemented in the in-house code DD3TRIM. The IVR method fundaments consists on the premise that state variables in all points associated to a Gauss volume of a given element are equal to the state variable quantities placed in the correspondent Gauss point. Hence, given a typical remapping procedure between a donor and a target mesh, the variables to be associated to a target Gauss volume (and point) are determined by a weighted average. The weight function is the Gauss volume percentage of each donor element that is located inside the target Gauss volume. The calculus of the intersecting volumes between the donor and target Gauss volumes is attained incrementally, for each target Gauss volume, by means of a discrete approach. The other two remapping strategies selected are based in the interpolation/extrapolation of variables by using the finite element shape functions or moving least square interpolants. The performance of the three different remapping strategies is address with two tests. The first remapping test was taken from a literature work. The test consists in remapping successively a rotating symmetrical mesh, throughout N increments, in an angular span of 90º. The second remapping error evaluation test consists of remapping an irregular element shape target mesh from a given regular element shape donor mesh and proceed with the inverse operation. In this second test the computation effort is also measured. The results showed that the error level associated to IVR can be very low and with a stable evolution along the number of remapping procedures when compared with the other two methods. Besides, the method proved to be very robust even in critical remapping situations such as poor geometrical definition of the mesh domain boundaries.

Keywords: Remapping, Mesh Transfer Operator, Numerical Simulation, Deep-Drawing, Error Evaluation, Incremental Volumetric Remapping.

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