On inverse form finding for orthotropic plasticity

• Autorzy: Landkammer P. , Germain S. , Steinmann P.
• Języki publikacji: EN

Abstrakty

EN

Inverse form finding aims to determine the optimum blank design of a workpiece whereby the desired spatial configuration that is obtained after a forming process, the boundary conditions and the applied loads are known. Inputting the optimal material configuration, a subsequent FEM computation then has to result exactly in the nodal coordinates of the desired deformed workpiece. Germain et al. recently presented a new form finding strategy for isotropic elastoplasticity. Switching between the direct and the inverse mechanical formulation, while fixing the internal plastic variables in the inverse step, uniquely detects the undeformed configuration iteratively. In this contribution, the developed recursive algorithm is extended to anisotropic plasticity. In particular the orthotropic Hill yield function is considered. A load and a displacement-controlled example demonstrate that this new strategy requires only a few iterations to determine the optimal initial design whereby an almost linear convergence rate is obtained.

Słowa kluczowe

EN

inverse FEM; inverse form finding; orthotropic Hill yield; logarithmic strain space; optimum blank design

PL

odwrócona metoda elementów skończonych; wydajność Hilla; odkształcona przestrzeń logarytmiczna

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Methods in Engineering and Science
• Rocznik: 2013
• Tom: Vol. 20, no. 4
• Strony: 337--348
• Opis fizyczny: Bibliogr. 20 poz., rys., tab., wykr.

Twórcy

autor

Landkammer P.

• Chair of Applied Mechanics, University Erlangen-Nuremberg Egerlandstrasse 5, 91058 Erlangen, Germany

autor

Germain S.

• Chair of Applied Mechanics, University Erlangen-Nuremberg Egerlandstrasse 5, 91058 Erlangen, Germany

autor

Steinmann P.

• Chair of Applied Mechanics, University Erlangen-Nuremberg Egerlandstrasse 5, 91058 Erlangen, Germany

Bibliografia

• [1] S. Germain, P. Landkammer, P. Steinmann. On a recursive formulation for solving inverse form finding problems in isotropic elastoplasticity. Advanced Modeling and Simulation in Engineering Sciences, submitted in 2013.
• [2] S. Germain, P. Steinmann. Shape optimization for anisotropic elastoplasticity in logarithmic strain space. Proceedings of the XIth Int. Conf. on Computational Plasticity, ISBN: 978-84-89925-73-1, 1479–1490, 2011.
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• [5] M. Scherer, R. Denzer, P. Steinmann. A fictious energy approach for shape optimization. Int. J. Numer. Meth. Eng., 82: 269–302, 2010.
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• [8] S. Germain, M. Scherer, P. Steinmann. On inverse form finding for anisotropic hyperelasticity in the logarithmic strain space. International Journal of Structural Changes in Solids, 2(2): 1–16, 2011.
• [9] S. Germain, P. Steinmann. A comparison between inverse form finding and shape optimization methods for anisotropic hyperelasticity in the logarithmic strain space. Proc. Appl. Math. Mech. (PAMM), 11: 367–368, 2011.
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• [19] S. Germain. On inverse form finding for anisotropic materials in the logarithmic strain space. PhD dissertation, University of Erlangen, 2013.
• [20] E. Lehmann, S. Schmaltz, S. Germain, D. Fassmann, C. Weber, S. Loehnert, M. Schaper, F.-W. Bach, P. Steinmann, K. Willner, P. Wriggers. Material model identification for DC04 based on the numerical modelling of the polycrystalline microstructure and experimental data. Key Engineering Materials, 504–506: 993–998, 2012.