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Reuleaux plasticity: analytical backward Euler stress integration and consistent tangent

Coombs, W.M.; Crouch, R.S.; Augarde, C.E

Reuleaux plasticity: analytical backward Euler stress integration and consistent tangent Thumbnail


Authors

R.S. Crouch



Abstract

Analytical backward Euler stress integration is presented for a deviatoric yielding criterion based on a modified Reuleaux triangle. The criterion is applied to a cone model which allows control over the shape of the deviatoric section, independent of the internal friction angle on the compression meridian. The return strategy and consistent tangent are fully defined for all three regions of principal stress space in which elastic trial states may lie. Errors associated with the integration scheme are reported. These are shown to be less than 3% for the case examined. Run time analysis reveals a 2.5–5.0 times speed-up (at a material point) over the iterative Newton–Raphson backward Euler stress return scheme. Two finite-element analyses are presented demonstrating the speed benefits of adopting this new formulation in larger boundary value problems. The simple modified Reuleaux surface provides an advance over Mohr–Coulomb and Drucker– Prager yield envelopes in that it incorporates dependencies on both the Lode angle

Citation

Coombs, W., Crouch, R., & Augarde, C. (2010). Reuleaux plasticity: analytical backward Euler stress integration and consistent tangent. Computer Methods in Applied Mechanics and Engineering, 199(25-28), 1733-1743. https://doi.org/10.1016/j.cma.2010.01.017

Journal Article Type Article
Publication Date Jan 1, 2010
Deposit Date May 4, 2010
Publicly Available Date Mar 6, 2015
Journal Computer Methods in Applied Mechanics and Engineering
Print ISSN 0045-7825
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 199
Issue 25-28
Pages 1733-1743
DOI https://doi.org/10.1016/j.cma.2010.01.017
Keywords Closest point projection, Computational plasticity, Analytical stress return, Energy-mapped stress space, Consistent tangent.
Public URL https://durham-repository.worktribe.com/output/1553016

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Copyright Statement
NOTICE: this is the author’s version of a work that was accepted for publication in Computer methods in applied mechanics and engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computer methods in applied mechanics and engineering., 199, 25-28, 2010, 10.1016/j.cma.2010.01.017






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