Development of an inverse isogeometric methodology and its application in sheet metal forming process

Abstract

• The inverse isogeometric methodology with a new friction model is developed to estimate the initial blank. • The geometric modeling and deformation analysis are integrated and applied simultaneously to analyze the forming process. • The three-dimensional state of problem is converted to two-dimensional state by using the isogeometric transfer technique. • The governing equations are solved without concerning about pre-estimation results. • The presented model estimates the design parameters quickly in the initial stages of design. This paper proposes an inverse isogeometric analysis to estimate the blank and predict the strain distribution in sheet metal forming processes. In this study, the same NURBS basis functions are used for drawing a final part and analysis of the forming process. In other words, this approach requires only one modeling and analysis representation, in contrast to inverse FEM. This model deals with minimization of potential energy, deformation theory of plasticity, and infinitesimal deformation relations with considering a new non-uniform friction model. One advantage of the presented methodology is that the governing equations are solved in two-dimensional space without concerning about pre-estimation results. As a result, the convergence is guaranteed and the computation time decreases significantly which is important at the initial stages of design. Furthermore, by employing this model at the forming design stage, the effects of changing the final part geometry and material property can be simultaneously observed on the formability of the part. Moreover, the effects of isogeometric element size can be automatically studied on the solution accuracy. The capability of this method is demonstrated by presenting three examples including blank estimation of cylindrical cup, square box, and weld line movement in forming of tailor welded blanks. The results obtained by the presented model and those obtained by the forward FEM reveal reasonable accuracy with decreased computational costs.