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      • Local Interpolation for Tools Surface Description

        D.M. Neto,M.C. Oliveira,J.L. Alves,L.F. Menezes 한국소성가공학회 2010 기타자료 Vol.2010 No.6

        Surface description accuracy is of paramount importance when modeling contact problems. However, most finite element method (FEM) researchers still resort to polyhedral models to describe contact surfaces, which can oversimplify the original system by neglecting the curvature. A simple algorithm for interpolating discretized surfaces and recover the original geometry was recently proposed by Nagata [1]. The main idea behind this parametric surface description (subsequently named Nagata patch) is the quadratic interpolation of a curved segment, from the position and normal vectors at the end points. The curved segment is used to recover the curvature of triangular or quadrilateral patches, defined by the vertices of the polyhedral mesh. This paper presents a study concerning the use of Nagata patches to local interpolate tools surface either defined by analytical functions or polyhedral models. The use of triangular or quadrilateral Nagata patches is compared, both in terms of efficiency and robustness of the local interpolation algorithm. Different strategies to approximate the tools normal defined by polyhedral models are presented and the error in the local interpolation is evaluated.

      • Local Bifurcation and Instability Theory Applied to Formability Analysis

        B.D. Buco,M.C. Oliveira,J.L. Alves,L.F. Menezes,K. Ito,N. Mori 한국소성가공학회 2010 기타자료 Vol.2010 No.6

        Sheet metal forming components are typically studied with the aid of finite element method based virtual tryout tools, since they allow to save money, time and effort in the design, production and process set-up of deep drawn parts. In all these development phases the analysis of defects is performed with the aid of the material forming limit diagram (FLD), since it allows defining a safe region that reduces: (i) necking; (ii) wrinkling and (iii) large deformation occurrence. It is known that the FLD represented in the strain space presents some disadvantages. The local bifurcation criterion proposed by Ito and Goya defines the critical state for a local bifurcation to set in, as a function of the stress level to work-hardening rate ratio. Thus, the main advantage is that the FLD represented in the stress plane is completely objective [1]. In this work the Ito and Goya model is used to evaluate formability, as well fracture mode and direction along different strain paths: (i) uniaxial tension; (ii) equibiaxial stretch; and (iii) plane-strain. All numerical simulations are performed with the in-house code DD3IMP [2, 3] and NXT [4] in which the Ito and Goya model is implemented, is applied to analyze the results.

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