Two Efficient Algorithms of Plastic Integration for Sheet Forming Modeling

[+] Author and Article Information
Y. M. Li, B. Abbès, Y. Q. Guo

Laboratory of Mechanics, Materials & Structures, Faculty of Sciences, University of Reims, BP1039, 51687, Reims, France

J. Manuf. Sci. Eng 129(4), 698-704 (Feb 13, 2007) (7 pages) doi:10.1115/1.2738125 History: Received July 20, 2006; Revised February 13, 2007

A fast method called the “inverse approach” for sheet forming modeling is based on the assumptions of the proportional loading and simplified tool actions. To improve the stress estimation, the pseudo-inverse approach was recently developed: some realistic intermediate configurations are geometrically determined to consider the deformation paths; two new efficient algorithms of plastic integration are proposed to consider the loading history. In the direct scalar algorithm (DSA), an elastic unloading-reloading factor γ is introduced to deal with the bending-unbending effects; the equation in unknown stress vectors is transformed into a scalar equation using the notion of the equivalent stress, thus the plastic multiplier Δλ can be directly obtained without iterative resolution scheme. In the γ-return mapping algorithm, the equivalent plastic strain increment estimated by DSA is taken as the initial solution in Simo’s return mapping algorithm, leading to a stable, efficient, and accurate plastic integration scheme. The numerical experience has shown that these two algorithms give a considerable reduction of CPU time in the plastic integration.

Copyright © 2007 by American Society of Mechanical Engineers
Topics: Stress , Algorithms , Scalars
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Figure 1

Determination of an intermediate configuration by minimization of sheet surface

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Figure 2

Intermediate configurations of SWIFT

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Figure 3

Distorted mesh obtained by surface minimization (H=7mm)

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Figure 4

Mapping of mesh Di onto mesh Ci to obtain a regular mesh with the correct shape

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Figure 7

Geometry of the SWIFT drawing process

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Figure 8

Plastic integration on a great increment with bending-unbending effect

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Figure 9

N-R convergence given by Simo’s RMA and the present γ-RMA

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Figure 11

Thickness distribution along the radial direction (h0=1mm)

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Figure 12

Punch force in function of punch travel

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Figure 14

Distribution of the maximal stress along the radial direction on the lower fiber

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Figure 15

Distribution of the maximal stress along the radial direction on the upper fiber

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Figure 13

von Mises stress distribution along the radial direction on the middle surface

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Figure 10

Thickness distribution obtained by different codes

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Figure 6

Elastic unloading and reloading; elastic prediction and plastic correction

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Figure 5

Meshes before and after the mapping problem




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