Towards Inverse Form Finding Methods for a Deep Drawing Steel DC04

Germain, S. and Steinmann, P. (2012) Towards Inverse Form Finding Methods for a Deep Drawing Steel DC04. In: 15th Conference of the European Scientific Association on Material Forming, ESAFORM 2012, Erlangen, Germany, 14-16 Mar 2012, pp. 619-624. ISBN 9783037853665 (doi: 10.4028/www.scientific.net/KEM.504-506.619)

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Abstract

A challenge in the design of functional parts in metal forming processes is the determination of the initial, undeformed shape such that under a given load a part will obtain the desired deformed shape. An inverse mechanical or a shape optimization formulation might be used to solve this problem, which is inverse to the standard kinematic analysis in which the undeformed shape is known and the deformed shape unknown. The objective of the inverse mechanical formulation aims in the inverse deformation map that determines the (undeformed) material configuration, where the spatial (deformed) configuration and the mechanical loads are given. The shape optimization formulation predicts the initial shape in the sense of an inverse problem via successive iterations of the direct problem. In this paper, both methods are presented using a formulation in the logarithmic strain space. An update of the reference configuration of the sheet of metal during the optimization process is proposed in order to avoid mesh distortions. A first example showed the results obtained with both methods in isotropic hyperelasticity. A second example illustrated a simplified deep drawing computed with the shape optimization formulation in isotropic elastoplasticity. From the undeformed shapes obtained with both methods the deformed shapes are acquired with the direct mechanical formulation. Compared to the target deformed shape a minor difference in node coordinates is found. The computation time is lower with the inverse mechanical formulation in hyperelasticity. The update of the reference configuration in the shape optimization formulation allowed to avoid mesh distortions but increased the computational costs.

Item Type:Conference Proceedings
Additional Information:Key Engineering Materials: volume 504-506, 2012, pages 619-624.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Steinmann, Professor Paul
Authors: Germain, S., and Steinmann, P.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:Key Engineering Materials
ISSN:1013-9826
ISBN:9783037853665
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