Prediction of Springback in the Air Bending Process Using a Kriging Metamodel


  • F. A. Khadra Faculty of Eng.-Rabigh, King Abdulaziz University, Saudi Arabia
  • A. W. El-Morsy Faculty of Eng.-Rabigh, King Abdulaziz University, Saudi Arabia | Faculty of Eng.-Helwan, Helwan University, Egypt
Volume: 6 | Issue: 5 | Pages: 1200-1206 | October 2016 |


This paper addresses the use of the kriging‏ approach to predict the springback in the air bending process. The materials and the geometrical parameters, which significantly affect the springback, were considered as inputs, and the springback angle was considered as the response. A verified nonlinear finite element model was used to generate the training data required to create the kriging‏ metamodel. The training examples were selected based on computer-generated D-optimal designs. A comparison between the kriging approaches and the response surface methodology is conducted and discussed. The results showed that kriging accurately predicts the finite element springback results. Comparing the accuracy of kriging with a response surface methodology shows that kriging with a 2nd degree polynomial and exponential correlation function predicts the springback more accurately than the response surface methodology.


Metamodels, Springback, Kriging, Response Surface Methodology, D-Optimal Designs


Download data is not yet available.


M. Osman, M. Shazly, A. El-Mokaddem, A. Wifi, “Springback prediction in V-die bending: modelling and experimentation”, J. Achiev. Mater. Manufac. Eng., Vol. 38, pp. 179-186, 2010

T. Botelho, E, Bayraktar, G. Inglebert, “Comparison of experimental and simulation results of 2D-draw-bend spring-back”, J. Achiev. Mater. Manufac. Eng., Vol. 18, pp. 275-278, 2006

I. Ragai, D. Lazim, J. Nemes, “Anisotropy and springback in draw-bending of stainless steel 410: experimental and numerical study”, J. Mater. Proc. Techno., Vol. 166, pp. 116–127, 2005 DOI:

M. Sitar, F. Kosel, M. Brojan, “Numerical and experimental analysis of elastic–plastic pure bending and springback of beams of asymmetric cross-sections”, Int. J. Mech. Sci., Vol. 90, pp. 77-88, 2015 DOI:

F. Kosel, T. Videnic, T. Kosel, M. Brojan, “Elasto-plastic springback of beams subjected to repeated bending/unbending histories”, J. Mater. Eng. Perform., Vol. 20, pp. 846–854, 2011 DOI:

Y. Zhu, Y. Liu, H. Yang, H. Li, “Improvement of the accuracy and the computational efficiency of the springback prediction model for the rotary-draw bending of rectangular H96 tube”, Int. J. Mech. Sci., Vol. 66, pp. 224–232, 2012 DOI:

R. Kazan, M. Firat, A. Tiryaki, “Prediction of springback in wipe-bending process of sheet metal using neural network”, Materials & Design, Vol. 30, pp. 418–423, 2009 DOI:

A. Ghaei, “Numerical simulation of springback using an extended return mapping algorithm considering strain dependency of elastic modulus”, Int. J. Mech. Sci., Vol. 65, pp. 38–47, 2012 DOI:

E. Nakamachi, T. Honda, H. Kuramae, Y. Morita, T. Ohata, H. Morimoto, “Two-scale finite element analyses for bendability and springback evaluation based on crystallographic homogenization method”, Int. J. Mech. Sci., Vol. 80, pp. 109-121, 2014 DOI:

H. Kim, N. Nargundkar, T. Altan, “Prediction of bend allowance and springback in air bending”, J. Manufac. Sci. Eng., Vol. 129, pp. 342-351, 2006 DOI:

S. Panthi, N. Ramakrishnan, K. Pathak, J. Chouhan, “An analysis of springback in sheet metal bending using finite element method”, J. Mater. Proc. Techno., Vol. 186, pp. 120–124, 2007 DOI:

I. Vladimirov, M. Nargundkar, S. Reese, “Prediction of springback in sheet forming by a new finite strain model with nonlinear kinematic and isotropic hardening”, J. Mater. Proc. Techno., Vol. 209, pp. 4062-4075, 2009 DOI:

R. Srinivasan, D. Vasudevan, A. Padmanabhan, “Prediction of spring-back and bend force in air bending of electro-galvanised steel sheets using artificial neural networks”, Aust. J. Mech. Eng., Vol. 12, pp. 25-37, 2014 DOI:

H. Baseri, B. Rahmani, Bakhshi-JM, “Predictive Models of the Spring-Back in the Bending Process, Applied Artificial Intelligence”, Appl. Artificial. Intell., Vol. 26, pp. 862–877, 2012 DOI:

L. Wang, G. Huang, H. Zhang, Y. Wang, L. Yin, “Evolution of springback and neutral layer of AZ31B magnesium alloy V-bending under warm forming conditions”, J. Mater. Proc. Techno., Vol. 213, pp. 844–850, 2013 DOI:

D. Zhang, Z. Cui, X. Ruan, Y. Li, “An analytical model for predicting springback and side wall curl of sheet after U-bending”, Compu. Mater. Sci., Vol. 38, pp. 707–715, 2007 DOI:

M. Firat, “U-Channel Forming Analysis with an Emphasis on Springback Deformation”, Materials & Design, Vol. 28, pp. 147-154, 2007 DOI:

P. Chen, M. Koç, “Simulation of springback variation in forming of advanced high strength steels”, J. Mater. Proc. Techno., Vol. 190, pp. 189–198, 2007 DOI:

G. Sharad, V. Nandedkar, “Springback in Sheet Metal U Bending-FEA and Neural Network”, Approach Procedia Mater. Sci. Vol. 6, pp. 835-839, 2014 DOI:

A. Mkaddem, D. Saidane, “Experimental approach and RSM procedure on the examination of springback in wiping-die bending processes”, J. Mater. Proc. Techno., Vol. 189, pp. 325–333, 2007 DOI:

T. Zou, J. Xin, D, Li, Q. Ren, “Analytical approach of springback of arced thin plates bending”, Procedia Eng., Vol. 81, pp. 993–998, 2014 DOI:

S. Feifei, Y. He, L. Heng, Z. Mei, L. Guangjun, “Springback prediction of thick-walled high-strength titanium tube bending”, Chinese J. Aeronautics, Vol. 26, pp. 1336–1345, 2013 DOI:

X. Yang, C. Choi, N. Sever, T. Altan, “Prediction of springback in air-bending of Advanced High Strength steel (DP780) considering Young's modulus variation and with a piecewise hardening function”, Int. J. Mech. Sci., Vol. 105, pp. 266–272, 2016 DOI:

J. Lee, F. Barlat, M. Lee, “Constitutive and friction modeling for accurate springback analysis of advanced high strength steel sheets”, Int. J. Plasticity, Vol. 71, pp. 113-135, 2015 DOI:

M. Tisza, Z. Lukacs, “Springback analysis of high strength dual-phase steels”, Procedia Eng., Vol. 81, pp. 975-980, 2014 DOI:

S. Panthi, N. Ramakrishnan, “Semi analytical modeling of springback in arc bending and effect of forming load”, Trans. Nonferrous Met. Soc. China, Vol. 21, pp. 2276−2284, 2011 DOI:

N. Nanu, G. Brabie, “Analytical model for prediction of springback parameters in the case of U stretch–bending process as a function of stresses distribution in the sheet thickness”, Int. J. Mech. Sci., Vol. 64, pp. 11–21, 2012 DOI:

X. Xue, J. Liao, G. Vincze, J. Gracio, “Modelling of mandrel rotary draw bending for accurate twist springback prediction of an asymmetric thin-walled tube”, J. Mater. Proc. Techno., Vol. 216, pp. 405–417, 2015 DOI:

M. Lee, J. Kim, K. Chung, S. Kim, R. Wagoner, H. Kim, “Analytical springback model for lightweight hexagonal close-packed sheet metal”, Int. J. Plasticity, Vol. 25, pp. 399–419, 2009 DOI:

V. Esat, H. Darendeliler, M. Gokler, “Finite element analysis of springback in bending of aluminium sheets”, Materials & Design, Vol. 23, pp. 223-229, 2002 DOI:

S. Lee, D. Yang, “An assessment of numerical parameters influencing springback in explicit finite element analysis of sheet metal forming process”, J. Mater. Proc. Techno., Vol. 80, pp. 60-67, 1998 DOI:

K. Li, W. Carden, R. Wagoner, “Simulation of springback”, Int. J. Mech. Sci., Vol. 44, pp. 103–122, 2002 DOI:

L. De-Vin, “Curvature prediction in air bending of metal sheet”, J. Mater. Proc. Techno., Vol. 100, pp. 257-261, 2000 DOI:

C. Díaz, M. Victoria, O. Querin, P. Martí, “Optimum design of semi-rigid connections using metamodels”, J. Constructional Steel Res., Vol. 78, pp. 97–106, 2012 DOI:

A. Khuri, J. Cornell, Response Surfaces: designs and analyses, 2nd ed. New York ISBN 0-8247-9781-8, 1996

D. Allaix, V. Carbone, “An improvement of the response surface method”, Structural Safety, Vol. 33, pp. 165–172, 2011 DOI:

A. Taflanidis, “Stochastic subset optimization incorporating moving least squares response surface methodologies for stochastic sampling”, Adv. Eng. Soft., Vol. 44, pp. 3–14, 2012 DOI:

F. Abu-Khadra, J. Abu-Qudeiri, “Comparison between neural network and response surface metamodels based on D–optimal designs”, Int. J. Compu. Mater. Sci. Sur. Eng., Vol. 5, pp. 85-101, 2013 DOI:

M. Ali-Tavoli, N. Nariman, A. Khakhali, “Multi-objective optimization of abrasive flow machining processes using polynomial neural networks and genetic algorithms”, Mach. Sci. Techno., Vol. 10, pp. 491–510, 2006 DOI:

M. Naseri, F. Othman, “Determination of the length of hydraulic jumps using artificial neural networks”, Adv. Eng. Soft., Vol. 48, pp. 27–31, 2012 DOI:

V. Papadopoulos, D. Giovanis, N. Lagaros, M. Papadrakakis, “Accelerated subset simulation with neural networks for reliability analysis”, Compu. Meth. Appl. Mech. Eng. Vol. 223, pp. 70-80, 2012 DOI:

R. Narayanasamy, P. Padmanabhan, “Comparison of regression and artificial neural network model for the prediction of springback during air bending process of interstitial free steel sheet”, J. Intelligent Manufacturing, Vol. 23, pp. 357-364, 2012 DOI:

H. Sun, M. Schafer, “Reduced order model assisted evolutionary algorithms for multi-objective flow design optimization”, Engineering Optimization, Vol. 43, pp. 97–114, 2011 DOI:

F. Magoules, L. Diago, I. Hagiwara, “Efficient preconditioning for image reconstruction with radial basis functions”, Adv. Eng. Soft., Vol. 38, pp. 320–327, 2007 DOI:

H. Safikhani, A. Khalkhali, M. Farajpoor, “Pareto based multi-objective optimization of centrifugal pumps using CFD, neural networks and genetic algorithms”, Engineering Applications of Computational Fluid Mechanics, Vol. 5, pp. 37-48, 2011 DOI:

J. C. Kleijnen, Design and Analysis of Simulation Experiments; 2nd ed. Springer, 2015. DOI:

N. Cressie, “The Origins of Kriging”, Math. Geo., Vol. 22, pp. 239-252, 1990. DOI:

B. Echard, N. Gayton, M. Lemaire, “AK-MCS an active learning reliability method combining Kriging and Monte Carlo Simulation”, Structural Safety, Vol. 33, pp. 145–154, 2011 DOI:

B. Echard, N. Gayton, M. Lemaire, N. Relun, “A combined importance sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models”, Reliab. Eng. Sys. Saf., Vol. 111, pp. 232–240, 2013 DOI:

Z. Fu, M. Jianhua, “Springback prediction of high-strength sheet metal under air bending forming and tool design based on GA–BPNN”, Int. J. Adv. Manufac. Techno., Vol. 53, pp. 473-483, 2011 DOI:

S. Chen, X. Hong, C. Harris, “Regression based D-optimality experimental design for sparse kernel density estimation”, Neurocomputing, Vol. 73, pp. 727–739, 2010 DOI:


How to Cite

F. A. Khadra and A. W. El-Morsy, “Prediction of Springback in the Air Bending Process Using a Kriging Metamodel”, Eng. Technol. Appl. Sci. Res., vol. 6, no. 5, pp. 1200–1206, Oct. 2016.


Abstract Views: 809
PDF Downloads: 318 Language Editing Certificate Downloads: 0

Metrics Information

Most read articles by the same author(s)