Article

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

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.

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Available from: C. Teodosiu, Jan 03, 2014
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    • "Indeed, the local support of the interpolation method allows to deal with hybrid surface meshes of arbitrary topology (irregular meshes composed by triangular and quadrilateral facets), which is the main feature of the proposed surface smoothing procedure. This interpolation method was previously applied to smooth rigid surfaces involved in 3D contact problems [50] [51] [52]. This work presents the extension of this interpolation method to deal with contact problems between deformable bodies, where the smoothed surface will suffer large deformations. "
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    ABSTRACT: This paper presents a contact surface smoothing method combined with the node-to-segment discretization technique to solve large deformation frictional contact problems between deformable bodies. The Nagata patch interpolation is used to smooth the surface mesh, providing a master surface with quasi-G1 continuity between patches. Moreover, the local support of the interpolation method allows to deal with surface meshes of arbitrary topology (regular and irregular finite element discretizations), as well as hybrid meshes. The non-physical oscillations in the contact force evolution, induced by the faceted contact surface representation, are reduced using the proposed smoothing method. Furthermore, the smooth representation of the master surface allows a more accurately evaluation of the resulting stresses and forces, while providing an important improvement in convergence behaviour. Four representative numerical examples are used to demonstrate the advantages of the proposed contact smoothing method. The results show a significant improvement in the accuracy, robustness and performance of the numerical simulations using the smoothing approach, when compared with the piecewise faceted contact surface description.
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    • "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. "
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    • "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. "
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    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.
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