1990
DOI: 10.1002/nme.1620290208
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Studies in anisotropic plasticity with reference to the Hill criterion

Abstract: SUMMARYAlgorithms based upon the notion of return mapping have been developed for the Hill yield function of anisotropic plasticity. The relative accuracy of two algorithms is assessed by means of iso-error maps. The choice of the algorithm turns out to be much more critical for the orthotropic Hill criterion than for the underlying isotropic von Mises plasticity model. A tangent operator that is consistent with the developed integration algorithm is formulated and its efficiency is assessed compared with the … Show more

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Cited by 113 publications
(47 citation statements)
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“…The history parameters corresponding to these two mechanisms are, respectively, the deviatoric strain invariant Ä p and the volumetric strain invariant ‡ p vol; c . Accordingly, the ow rule, Equation (19), can be decomposed into a frictional contribution and a compaction contribution, which, in accordance with Koiter's generalization theorem [14], yields …”
Section: Cyclic Densification Modelmentioning
confidence: 97%
“…The history parameters corresponding to these two mechanisms are, respectively, the deviatoric strain invariant Ä p and the volumetric strain invariant ‡ p vol; c . Accordingly, the ow rule, Equation (19), can be decomposed into a frictional contribution and a compaction contribution, which, in accordance with Koiter's generalization theorem [14], yields …”
Section: Cyclic Densification Modelmentioning
confidence: 97%
“…In the present work, the return mapping algorithm is based on the closest point projection procedure by Simo and Taylor [17] and the algorithm proposed by Borst and Feenstra [18] for Hill's quadratic normal anisotropic yield function. In-plane stress and strain are updated during the return mapping iterations using the yield function expanded by the transverse normal stress.…”
Section: Integration Algorithmmentioning
confidence: 99%
“…Otherwise the trial stress is invalid and needs to be returned to the yield surface. Therefore a return mapping algorithm according to [3] is utilized.…”
Section: Materials Modelmentioning
confidence: 99%