Adaptive through-thickness integration for accurate springback prediction. (English) Zbl 1195.74163
Summary: Accurate numerical prediction of springback in sheet metal forming is essential for the automotive industry. Numerous factors influence the accuracy of prediction of this complex phenomenon by using the finite element method. One of them is the numerical integration through the thickness of shell elements. It is known that the traditional numerical schemes are very inefficient in elastic – plastic analysis and even for simple problems they require up to 50 integration points for an accurate springback prediction. An adaptive through-thickness integration strategy can be a good alternative. The main characteristic feature of the strategy is that it defines abscissas and weights depending on the integrand’s properties and, thus, can adapt itself to improve the accuracy of integration. A concept of an adaptive through-thickness integration strategy for shell elements is presented in this paper. Its potential is demonstrated using two examples. Calculations of a simple test – bending a beam under tension – show that for a similar set of material and process parameters the adaptive rule with seven integration points performs significantly better than the traditional trapezoidal rule with 50 points. Simulations of an unconstrained cylindrical bending problem demonstrate that the adaptive through-thickness integration strategy for shell elements can guarantee an accurate springback prediction at minimal costs.
References:
| [1] | Li, Simulation of springback, International Journal of Mechanical Sciences 44 (1) pp 103– (2002) · Zbl 0986.74522 |
| [2] | Meinders, A sensitivity analysis on the springback behavior of the unconstrained bending, International Journal of Forming Processes 9 (3) pp 365– (2006) |
| [3] | Li K, Geng L, Wagoner RH. Simulation of springback: choice of element. In Proceedings of Advanced Technology of Plasticity, Geiger M (ed.), Nuremberg, Germany, 1999; 2091–2099. |
| [4] | Carleer BD, Meinders T, Pijlman HH, Huétink J, Vegter H. A planar anisotropic yield function based on multi axial stress states in finite elements. In Proceedings of Complas’97, Owen DRJ, Onate E, Hinton E (eds), Barcelona, Spain, 1997; 913–920. |
| [5] | Yoshida, A model of large-strain cyclic plasticity and its application to springback simulation, International Journal of Mechanical Sciences 45 (10) pp 1687– (2003) · Zbl 1049.74014 |
| [6] | Oliveira MC, Alves JL, Chaparro BM, Menezes LF. Study on the influence of the work hardening models constitutive parameters identification in the springback prediction. In Proceedings of the 6th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes, Numisheet 2005, Smith LM, Pourboghrat F, Yoon JW, Stoughton TB (eds), Detroit, U.S.A., 2005; 253–258. |
| [7] | Cleveland, Inelastic effects on springback in metals, International Journal of Plasticity 18 (5–6) pp 769– (2002) · Zbl 0995.74501 |
| [8] | Teodosiu C. Some basic aspect of the constitutive modelling in sheet metal forming. In Proceedings of the 8th ESAFORM Conference on Material Forming, Banabic D (ed.), Cluj-Napoca, Romania, 2005; 239–243. |
| [9] | Krasowsky A, Walde T, Schmitt W, Andrieux F, Riedel H. Springback simulation in sheet metal forming using material formulation based on combined isotropic–kinematic hardening with elastic–plastic anisotropy. In Proceedings of IDDRG 2004, Kergen R, Kebler L, Langerak N, Lenze F-J, Janssen E, Steinbeck G (eds), Sindelfingen, Germany, 2004; 104–113. |
| [10] | Park, A four-node shell element with enhanced bending performance for springback analysis, Computer Methods in Applied Mechanics and Engineering 193 (23–26) pp 2105– (2002) |
| [11] | Burchitz IA, Meinders T, Huétink J. Influence of numerical parameters on springback prediction in sheet metal forming. In Proceedings of the 9th International Conference on Material Forming, ESAFORM 2006, Juster N, Rosochowski A (eds), Glasgow, U.K., 2006; 407–410. |
| [12] | Burgoyne, Numerical integration strategy for plates and shells, International Journal for Numerical Methods in Engineering 29 (1) pp 105– (1990) · Zbl 0724.73287 |
| [13] | Harn, Adaptive multi-point quadrature for elastic–plastic shell elements, Finite Elements in Analysis and Design 30 (4) pp 253– (1998) · Zbl 0922.73059 |
| [14] | Wagoner, Simulation of springback: through-thickness integration, International Journal of Plasticity 23 (3) pp 345– (2007) · Zbl 1349.74378 · doi:10.1016/j.ijplas.2006.04.005 |
| [15] | Atkinson, An Introduction to Numerical Analysis (1989) · Zbl 0718.65001 |
| [16] | Davis, Methods of Numerical Integration (1985) |
| [17] | Carleer B. Finite element analysis of deep drawing. Ph.D. Thesis, University of Twente, Enschede, 1997. |
| [18] | Cook, Concepts and Applications of Finite Element Analysis (2002) |
| [19] | Belytschko, Nonlinear Finite Elements for Continua and Structures (2000) |
| [20] | Rajendran, Optimal stress sampling points of plane triangular elements for patch recovery of nodal stresses, International Journal for Numerical Methods in Engineering 58 (4) pp 579– (2003) · Zbl 1032.74679 |
| [21] | Wagoner RH, Li M. Advances in springback. In Proceedings of the 6th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes, Numisheet 2005, Smith LM, Pourboghrat F, Yoon JW, Stoughton TB (eds), Detroit, U.S.A., 2005; 209–214. |
| [22] | Rice, A metalgorithm for adaptive quadrature, Journal of the ACM 22 (1) pp 61– (1975) |
| [23] | Gander, Adaptive quadrature–revisited, BIT Numerical Mathematics 40 (1) pp 84– (2000) · Zbl 0961.65018 |
| [24] | Espelid, Doubly adaptive quadrature routines based on Newton–Cotes rules, BIT Numerical Mathematics 43 (2) pp 319– (2003) · Zbl 1034.65017 |
| [25] | Van den Boogaard, Efficient implicit finite element analysis of sheet forming processes, International Journal for Numerical Methods in Engineering 56 (8) pp 1083– (2003) · Zbl 1078.74669 |
| [26] | Oliveira MC, Alves JL, Menezes LF. Springback evaluation using 3-D finite elements. In Proceedings of the 5th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes, Numisheet 2002, Yang D-Y, Oh SI, Huh H, Kim YH (eds), Jeju Island, Korea, 2002; 189–194. |
| [27] | Papeleux, Finite element simulation of springback in sheet metal forming, Journal of Materials Processing Technology 125–126 pp 785– (2002) |
| [28] | Armen H, Pifko A, Levine HS. Finite element analysis of structures in the plastic range. Technical Report, Grumman Aerospace Corporation, 1971. |
| [29] | NUMISHEET’93. Proceedings of the 2nd International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes, Numisheet 1993, Makinouchi A, Nakamachi E, Onate E, Wagoner RH (eds), Isehara, Japan, 1993. |
| [30] | Avetisyan, Influence of an accurate trimming operation on springback, International Journal of Forming Processes pp 31– (2005) |
| [31] | Burchitz IA. Simplified adaptive through-thickness integration strategy for shell elements. Internal Report, Netherlands Institute for Metals Research–University of Twente, 2007. |
| [32] | NUMISHEET’02. In Proceedings of the 5th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes, Numisheet 2002, Yang D-Y, Oh SI, Huh H, Kim YH (eds), Jeju Island, Korea, 2002. |
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