Convexity of Yield Surface with Directional Distortional Hardening Rules
Publication: Journal of Engineering Mechanics
Volume 136, Issue 4
Abstract
The present paper examines the convexity of the yield surface in the directional distortional hardening models by Feigenbaum and Dafalias. In these models anisotropy develops through kinematic and directional distortional hardening, supplemented by the classical isotropic hardening, and the associative flow rule is used. However, the issue of convexity, which naturally arises due to the distortion of the yield surface, was not fully addressed. The present paper derives the necessary and sufficient conditions to ensure convexity of the yield surface for the simpler Feigenbaum and Dafalias models, but it is not as straightforward to derive corresponding conditions for convexity of the Feigenbaum and Dafalias model version which contains an evolving fourth-order tensor. In this case convexity will be addressed first in general and then at the limit state for which simple restrictions on the material constants to ensure convexity are derived. Numerical examples will show that some of the yield surfaces simulated in the original Feigenbaum and Dafalias publication will not stay convex if loaded beyond what was done in these publications. Therefore the material constants for these cases are recalibrated based on the derived relations for satisfaction of the convexity requirement, and the fitting of the yield surfaces is repeated with the new set of constants and compared with the previous case.
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Acknowledgments
This work was supported by GA CR 101/09/1630 under AV0Z20760514. The writers thank the reviewers for their helpful observations, in particular the one which lead to the consideration of the and − signs appearing in the third member of Eq. (25) and the equations that follow.
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Published In
Journal of Engineering Mechanics
Volume 136 • Issue 4 • April 2010
Pages: 477 - 484
Copyright
© 2010 ASCE.
History
Received: Mar 3, 2009
Published online: Aug 8, 2009
Accepted: Sep 21, 2009
Published in print: Apr 2010
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