Application of a Non-Invasive Form Finding Algorithm to the Ring Compression Test with Varying Friction Coefficients

Abstract

It is a great challenge in the development of functional components to determine the optimal blank design (material configuration) of a workpiece according to a specific forming process, while knowing the desired target geometry (spatial configuration). A new iterative non-invasive algorithm, which is purely based on geometrical considerations, is developed to solve inverse form finding problems. The update-step is performed by mapping the nodal spatial difference vector, between the computed spatial coordinates and the desired spatial target coordinates, with a smoothed deformation gradient to the discretized material configuration. The iterative optimization approach can be easily coupled non-invasively via subroutines to arbitrary finite element codes such that the pre-processing, the solving and the post-processing can be performed by the habitual simulation software. This is exemplary demonstrated by an interacting between Matlab (update procedure for inverse form finding) and MSC.MarcMentat (metal forming simulation). The algorithm succeeds for a parameter study of a ring compression test within nearly linear convergence rates, despite highly deformed elements and tangential contact with varying friction parameters.