  The 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 that require severe deformation and
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. Besides, the presented methodology can 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 experimentally
and numerically evaluated under two classical problems, including the forming
of a rectangular box and a two-step drawing of a circular cup. Results
comparisons indicate the credibility of the presented model in prediction of
forming parameters at a low computation time.
