Some improvements on the one-step inverse isogeometric analysis by proposing a multi-step inverse isogeometric methodology in sheet metal stamping processes

Abstract

Recently, isogeometric methodology has been successfully implemented in one-step inverse analysis of sheet metal stamping processes. However, these models are not capable of analyzing forming processes which require severe deformation and/or several forming stages. This paper presents a multi-step inverse isogeometric methodology to enhance the precision of one-step models in predictions of the initial blank, strain distributions, and drawability of the formed parts. This methodology deals with the minimization of potential energy, deformation theory of plasticity, and considering membrane elements. The presented methodology utilizes the NURBS basis functions to create the final, middle, and blank geometries, and also to analyze sheet metal deformation. The characteristics of the applied formulations make it possible to simultaneously observe the effects of changing part parameters on its formability. One advantage of this approach is that the linear system of governing equations is solved without concerning about the convergence. In addition, the presented methodology is able to successfully generate the middle geometry and to restrict the movements of physical nodes along the middle surface, by presenting a new NURBS-based mapping and sliding constraint technique. The performance of the presented model is evaluated under two classical problems including forming of a rectangular box and a two-step drawing of a circular cup. In forming of the rectangular box, the results of the presented model are compared with those of experiment and forward FEM simulation. Also, in the second problem, the presented approach is only compared with forward FEM simulation. Results comparisons indicate the credibility of the presented model in prediction of forming parameters at a low computation time.