INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2008; 75:533–554 Published online 17 December 2007 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/nme.2260 Adaptive through-thickness integration for accurate springback prediction I. A. Burchitz 1, 2, ∗, † and T. Meinders 2 1 Netherlands Institute for Metals Research, P.O. Box 5008, 2600 GA Delft, The Netherlands 2 University of Twente, Faculty of Engineering Technology, P.O. Box 217, 7500AE Enschede, The Netherlands 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. Copyright 2007 John Wiley & Sons, Ltd. Received 3 May 2007; Revised 15 October 2007; Accepted 27 October 2007 KEY WORDS: sheet metal forming; springback; finite element methods; shells; adaptive quadrature 1. INTRODUCTION Springback prediction and compensation are one of the major challenges in the modern die manu- facturing industry. It is a common practice to use finite element software alongside engineering guidelines while designing new sheet metal parts. Based on results of the finite element analysis, ∗ Correspondence to: I. A. Burchitz, University of Twente, Faculty of Engineering Technology, P.O. Box 217, 7500AE Enschede, The Netherlands. † E-mail: i.burchitz@nimr.nl Contract/grant sponsor: Netherlands Institute for Metals Research Copyright 2007 John Wiley & Sons, Ltd.