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A comparative study of stress update algorithms for rate-independent and rate-dependent crystal plasticity

2000; Wiley; Volume: 50; Issue: 2 Linguagem: Inglês

10.1002/1097-0207(20010120)50

1097-0207

Christian Miehé, J�rg Schr�der,

Fatigue and fracture mechanics

International Journal for Numerical Methods in EngineeringVolume 50, Issue 2 p. 273-298 Research Article A comparative study of stress update algorithms for rate-independent and rate-dependent crystal plasticity Christian Miehe, Corresponding Author Christian Miehe cm@mechbau.uni.stuttgart.de Institut für Mechanik (Bauwesen) Lehrstuhl I, Universität Stuttgart, 70550 Stuttgart, Pfaffenwaldring 7, GermanyInstitut fur Mechanik (Bauwesen), Universität Stuttgart, Lehrstuhl I, Pfaffenwaldring 7, 70569 Stuttgart, GermanySearch for more papers by this authorJörg Schröder, Jörg Schröder Institut für Mechanik (Bauwesen) Lehrstuhl I, Universität Stuttgart, 70550 Stuttgart, Pfaffenwaldring 7, GermanySearch for more papers by this author Christian Miehe, Corresponding Author Christian Miehe cm@mechbau.uni.stuttgart.de Institut für Mechanik (Bauwesen) Lehrstuhl I, Universität Stuttgart, 70550 Stuttgart, Pfaffenwaldring 7, GermanyInstitut fur Mechanik (Bauwesen), Universität Stuttgart, Lehrstuhl I, Pfaffenwaldring 7, 70569 Stuttgart, GermanySearch for more papers by this authorJörg Schröder, Jörg Schröder Institut für Mechanik (Bauwesen) Lehrstuhl I, Universität Stuttgart, 70550 Stuttgart, Pfaffenwaldring 7, GermanySearch for more papers by this author First published: 18 December 2000 https://doi.org/10.1002/1097-0207(20010120)50:2 3.0.CO;2-QCitations: 82AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract The paper presents a comparative discussion of stress update algorithms for single-crystal plasticity at small strains. The key result is a new unified fully implicit multisurface-type return algorithm for both the rate-independent and the rate-dependent setting, endowed with three alternative approaches to the regularization of possible redundant slip activities. The fundamental problem of the rate-independent theory is the possible ill condition due to linear-dependent active slip systems. We discuss three possible algorithmic approaches to deal with this problem. This includes the use of alternative generalized inverses of the Jacobian of the currently active yield criterion functions as well as a new diagonal shift regularization technique, motivated by a limit of the rate-dependent theory. Analytical investigations and numerical experiments show that all three approaches result in similar physically acceptable predictions of the active slip of rate-independent single-crystal plasticity, while the new proposed diagonal shift method is the most simple and efficient concept. Copyright © 2001 John Wiley & Sons, Ltd. Citing Literature Volume50, Issue220 January 2001Pages 273-298 RelatedInformation