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On Optimization Strategies for Inverse Problems in Metalforming

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Sheet Bulk Metal Forming (TCRC73 2020)

Part of the book series: Lecture Notes in Production Engineering ((LNPE))

Abstract

In this contribution we consider inverse mechanical problems in terms of parameter identification and shape optimization. The fundamental material behavior is thereby modelled with an elasto-plastic constitutive law based on the logarithmic strain space, considering anisotropic yield and kinematic hardening. The identification of the constitutive material parameters is based on the virtual fields method (VFM) minimizing the gap between external and internal virtual work. By using a strategy with relation to a stress sensitivity analysis, the virtual fields can be obtained automatically. A specifically designed cruciform specimen, which produces heterogeneous deformation states, is used with a biaxial testing machine. For the shape optimization, a Newton iteration step is deduced to iteratively minimize the differences between desired and deformed shape of a forming simulation. The presented inverse, node-based algorithm covers a wide range of applications, since all requirements of a forming process are fulfilled. The method is demonstrated by means of a backward extrusion process.

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Acknowledgment

This study was supported by the German Research Foundation (DFG) within the scope of the Transregional Collaborative Research Centre for sheet-bulk metal forming (TCRC 73, Subproject C3). The authors are in addition grateful to all students who supported the realization of this work.

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Authors and Affiliations

  1. Institute of Applied Mechanics, Egerlandstraße 5, 91058, Erlangen, Germany

    Benjamin Söhngen, Michael Caspari, Kai Willner & Paul Steinmann

Authors
  1. Benjamin Söhngen
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  2. Michael Caspari
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  3. Kai Willner
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  4. Paul Steinmann
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Corresponding author

Correspondence to Benjamin Söhngen .

Editor information

Editors and Affiliations

  1. Lehrstuhl für Fertigungstechnologie, Friedrich-Alexander-Universität, Erlangen, Bayern, Germany

    Marion Merklein

  2. Institut für Umformtechnik & Leichtbau, Technische Universität Dortmund, Dortmund, Nordrhein-Westfalen, Germany

    A. Erman Tekkaya

  3. Institut für Umformtechnik und Umformmaschinen, Leibniz Universität Hannover, Garbsen, Niedersachsen, Germany

    Bernd-Arno Behrens

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Söhngen, B., Caspari, M., Willner, K., Steinmann, P. (2021). On Optimization Strategies for Inverse Problems in Metalforming. In: Merklein, M., Tekkaya, A.E., Behrens, BA. (eds) Sheet Bulk Metal Forming . TCRC73 2020. Lecture Notes in Production Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-61902-2_16

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  • DOI: https://doi.org/10.1007/978-3-030-61902-2_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-61901-5

  • Online ISBN: 978-3-030-61902-2

  • eBook Packages: EngineeringEngineering (R0)

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