Energy based algorithms to solve initial solution in one-step finite element method of sheet metal stamping

One-step finite element method (also called inverse approach) is more and more widely used in the automobile industry because of its unique advantages. Initial solution is an essential issue to ensure the success of the non-linear resolution in the implicit static one-step finite element solver. In order to speed up the convergence of the Newton–Raphson iterations, different kinds of initial solution methods are known. These are studied and compared in this paper. Several examples are followed to show their performance and efficiency. However most of these methods are based on geometric considerations like the geometric mapping method or the radial length development method. This kind of geometry based mapping methods could not reflect all aspects of the actual forming process. Therefore, an energy based mapping algorithm was implemented and coupled with the reverse deformation method which is based on the assumption of linear elastic deformation. This novel algorithm is proposed to provide the initial solution of one-step finite element method. For a complicated sheet forming modeling initial solutions obtained by different energy based algorithms coupled with the reverse deformation method are then compared in this paper. The results show that the Desbrun quadratic energy method and the accordant parameterization method combined with the inverse deformation method respectively are universal, efficient and robust initial solution schemes for the one-step finite element method.