Finite-element simulation of springback in sheet metal forming using local interpolation for tool surfaces

LPMTM-CNRS, University Paris 13, 93430 Villetaneuse, France
International Journal of Mechanical Sciences (Impact Factor: 2.06). 02/2008; DOI: 10.1016/j.ijmecsci.2007.07.005

ABSTRACT This paper describes new techniques for the sheet metal forming simulation using a local interpolation for tool surfaces proposed by Nagata [Simple local interpolation of surfaces using normal vectors. Computer Aided Geometric Design 2005;22:327–47] and the effect of tool modeling accuracy on springback simulation of a high strength steel sheet. The Nagata patch enables the creation of tool models that are much more accurate, in terms of not only shape but also normal vectors, than those of conventional polyhedral representations. Besides allowing an improved description of the contact between the sheet nodes and the tool surfaces, the proposed techniques have the advantage of relatively straightforward numerical implementation. Springback simulations of a two-dimensional draw bending process of a high strength steel sheet are then carried out using the polyhedral and Nagata patch models. It is found that the simulation results are largely influenced by the tool mesh when using polyhedral representations, while they are rather independent when using the Nagata patch representations. This demonstrates the efficiency and reliability of the numerical solution using the Nagata patch model.

  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: This paper presents a general 3D contact smoothing method based on the meshfree radial point interpolation method to improve the numerical simulation of contact problems. In particular, a locally smooth contact surface is constructed from the scattered surface nodes by point interpolation using the combination of polynomial and radial bases. With such bases, this method reproduces smooth surfaces even for coarse meshes and the constructed surface passes exactly through the surface nodes. Results for contact problems involving deformable bodies are included to demonstrate its advantages.
    Journal of Computational and Applied Mathematics 02/2014; 257:1-13. · 1.08 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: In the present study, the deformation behavior of a cast Mg alloy sheet that had random crystallographic orientations was studied both experimentally and numerically. Although the crystallographic orientations were random, the stress-strain curve was asymmetric between tension and compression: the flow stress under tension was higher than that of compression. Moreover, the stress-strain curve exhibited a strain path dependency: a slightly sigmoidal curve occurred under tension following compression, while it did not occur under compression following tension. Clearly, such tendencies were similar to those observed in rolled Mg alloy sheets although the tendencies were less pronounced in the cast Mg alloy sheet. A crystal plasticity finite-element method was used to understand the mechanism of these results. Simulation results showed that the asymmetry and the strain path dependency in the stress-strain curves occurred in the cast Mg alloy sheet because of the asymmetry in the activity of twinning between tension and compression as in the case of rolled Mg alloy sheets.
    Key Engineering Materials 05/2014; 611-612:27-32.
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: This study deals with different tool surface description methods used in the finite element analysis of sheet metal forming processes. The description of arbitrarily-shaped tool surfaces using the traditional linear finite elements is compared with two distinct smooth surface description approaches: (i) Bézier patches obtained from the Computer-Aided Design model and (ii) smoothing the finite element mesh using Nagata patches. The contact search algorithm is presented for each approach, exploiting its special features in order to ensure an accurate and efficient contact detection. The influence of the tool modelling accuracy on the numerical results is analysed using two sheet forming examples, the unconstrained cylindrical bending and the reverse deep drawing of a cylindrical cup. Smoothing the contact surfaces with Nagata patches allows creating more accurate tool models, both in terms of shape and normal vectors, when compared with the conventional linear finite element mesh. The computational efficiency is evaluated in this study through the total number of increments and the required CPU time. The mesh refinement in the faceted description approach is not effective in terms of computational efficiency due to large discontinuities in the normal vector field across facets, even when adopting fine meshes.
    International Journal of Material Forming 01/2014; · 1.42 Impact Factor


Available from
Jun 4, 2014