Finite-element simulation of springback in sheet metal forming using local interpolation for tool surfaces

This paper describes new techniques for the sheet metal forming simulation using a local interpolation for tool surfaces proposed by Nagata [Simple local interpolation of surfaces using normal vectors. Computer Aided Geometric Design 2005;22:327–47] and the effect of tool modeling accuracy on springback simulation of a high strength steel sheet. The Nagata patch enables the creation of tool models that are much more accurate, in terms of not only shape but also normal vectors, than those of conventional polyhedral representations. Besides allowing an improved description of the contact between the sheet nodes and the tool surfaces, the proposed techniques have the advantage of relatively straightforward numerical implementation. Springback simulations of a two-dimensional draw bending process of a high strength steel sheet are then carried out using the polyhedral and Nagata patch models. It is found that the simulation results are largely influenced by the tool mesh when using polyhedral representations, while they are rather independent when using the Nagata patch representations. This demonstrates the efficiency and reliability of the numerical solution using the Nagata patch model.