Adaptive through‐thickness integration for accurate springback prediction

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