Towards inverse form finding methods for a deep drawing steel DC04
Germain S, Steinmann P (2012)
Publication Type: Conference contribution
Publication year: 2012
Journal
Publisher: Trans Tech Publications
Edited Volumes: Key Engineering Materials
Book Volume: 504-506
Pages Range: 619-624
Conference Proceedings Title: 15th ESAFORM Conference Proceeding
Event location: Erlangen, Germany
DOI: 10.4028/www.scientific.net/KEM.504-506.619
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. © (2012) Trans Tech Publications.
Authors with CRIS profile
Sandrine Germain
Lehrstuhl für Technische Mechanik (LTM)
Paul Steinmann
Lehrstuhl für Technische Mechanik (LTM)
How to cite
APA:
Germain, S., & Steinmann, P. (2012). Towards inverse form finding methods for a deep drawing steel DC04. In 15th ESAFORM Conference Proceeding (pp. 619-624). Erlangen, Germany, DE: Trans Tech Publications.
MLA:
Germain, Sandrine, and Paul Steinmann. "Towards inverse form finding methods for a deep drawing steel DC04." Proceedings of the 15th ESAFORM Conference, Erlangen, Germany Trans Tech Publications, 2012. 619-624.
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