Semi-analytical approach for plane strain sheet metal forming using a bending-under-tension numerical model

In this paper, we revisit the plane strain deep-drawing process. We show that a detailed analysis of the physical process may result in a dramatic reduction of computing time when the problem is split into several regions undergoing well-defined loading paths. The proposed approach allows us to assess the springback of the formed sheet in a quasi-instant time and is thus suitable in the initial design phase and provides a fast and economical way to determine the influence of the numerous parameters involved in sheet metal forming. We present a semi-analytical model that has been developed for sheet metal forming mainly subjected to plane strain bending-under-tension and involving large strains. The sheet is considered to be an assembly of regions where the loading is considered homogeneous in the length direction. A handful of finite elements or even a single element is sufficient to compute the loading path followed by each region. The contact is circumvented by constraining the kinematics with appropriate boundary conditions and the approach is valid for any material behavior law. The semi-analytical model is applied to standard test cases and then compared with full-scale simulations.