Model adaptivity for industrial application of sheet metal forming simulation

In finite element simulation of sheet metal forming, shell elements are widely used. The limits of applicability of the shell elements are sometimes disregarded, which leads to an error in predictions of important values such as springback geometry. The underlying kinematic assumptions of the shell elements do not hold where the thickness of the metal sheet approaches the value of the radius of curvature. Complex three-dimensional material behavior effects cannot be represented precisely as the result of the simplified kinematics. Here we present a model adaptivity scheme based on a model error indicator. The model-adaptive technique presented in this paper aides to resolve only the critical areas of the structure with a three-dimensional discretization while keeping reasonable computational cost by utilizing shell elements for the rest of the structure. The model error indicator serves as a guide for subsequent automatic adaptive re-meshing of the work-piece followed by a model-adaptive finite element analysis. The accuracy of the approximation obtained by the model-adaptive technique coincides well with that of a more expensive solution obtained with solid elements only.