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: 2.03). 02/2008; 50(2):175-192. DOI: 10.1016/j.ijmecsci.2007.07.005


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.

Download full-text


Available from: C. Teodosiu, Jan 03, 2014
  • Source
    • "The Gregory patch augments the third-order Bézier patch with additional internal control points to enable tangent plane continuity in general. With special treatments [17] developed for patches involving inflection points, the Nagata patch interpolation algorithm can be applied to both triangular and quadrilateral faceted finite elements [18] [17] [19]. However, a consensual good solution for contact smoothing of complex surfaces composed of hybrid meshes (Fig. 1(d)), where each facet, surrounded by an arbitrary number of neighboring facets, can be either quadrilateral or triangular, remains a challenge. "
    [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. DOI:10.1016/ · 1.27 Impact Factor
  • Source
    • "In fact, the criteria considered required to develop an appropriate interpolation method for contact surface smoothing, according to [11], are entirely fulfilled by Nagata patch, being this a promising interpolation method to be applied in computational contact mechanics [18] [25]. The Nagata patch interpolation algorithm recovers the curvature of surfaces with good accuracy using the position and normal vectors of each vertex of the piecewise model. "
    [Show abstract] [Hide abstract]
    ABSTRACT: This paper presents an algorithm to accurately evaluate the surface normal vector in any vertex of a finite element mesh, in order to be able to efficiently apply the Nagata patch interpolation as surface mesh smoothing method when solving contact problems. The proposed algorithm considers that the surface geometry is also described by trimmed NURBS surfaces, with input data available in IGES file format. For each mesh vertex, the proposed approach comprises the following three steps: surface global search, local search, and normal vector evaluation. In the global search procedure, all trimmed NURBS surfaces composing the geometric model are ordered by proximity to the vertex. After that, local search is performed to find both the correct NURBS surface and the local coordinates of the vertex, which are defined by its projection on the selected surface. The vertex normal vector is them determined based on the first derivatives of the NURBS surface at the projection point. To highlight the feasibility of the developed algorithm, a mesh smoothing example is presented, emphasising the influence of the vertex normal vector approximation on the interpolation accuracy.
    Finite Elements in Analysis and Design 09/2013; DOI:10.1016/j.finel.2013.03.004 · 2.02 Impact Factor
  • Source
    • "The superscript T denotes the transpose. Assuming that all the rate-form relations are preserved from time t to t+∆t, where ∆t is a small time increment, an incremental form of the principle of virtual velocity can be written in the form (Kawka and Makinouchi, 1995; Hama et al., 2008 "
    [Show abstract] [Hide abstract]
    ABSTRACT: A crystal-plasticity finite-element analysis of the loading–unloading process under uniaxial tension of a rolled magnesium alloy sheet was carried out, and the mechanism of the inelastic response during unloading was examined, focusing on the effects of basal and nonbasal slip systems. The prismatic and basal slip systems were mainly activated during loading, but the activation of the prismatic slip systems was more dominant. Thus the overall stress level during loading was determined primarily by the prismatic slip systems. The prismatic slip systems were hardly activated during unloading because the stress level was of course lower than that during loading. On the other hand, because the strength of the basal slip systems was much lower than that of the prismatic slip systems, the basal slip systems would be easily activated under the stress level during unloading in the opposite direction when their Schmid’s resolved shear stresses changed signs because of the inhomogeneity of the material. These results indicated that one explanation for the inelastic behavior during unloading was that the basal slip systems were primarily activated owing to their low strengths compared to that of the prismatic slip systems. Numerical tests using the sheets with random orientations and with the more pronounced texture were conducted to further examine the mechanism.
    International Journal of Plasticity 07/2011; 27(7):1072-1092. DOI:10.1016/j.ijplas.2010.11.004 · 5.57 Impact Factor
Show more