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A return mapping algorithm for unified strength theory model
Author(s) -
Lin Chen,
Li YueMing
Publication year - 2015
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4937
Subject(s) - strength theory , algorithm , mohr–coulomb theory , principal component analysis , von mises yield criterion , mathematics , principal stress , stress (linguistics) , intersection (aeronautics) , geometry , space (punctuation) , plane stress , mathematical analysis , finite element method , structural engineering , engineering , computer science , cauchy stress tensor , physics , mechanics , linguistics , statistics , philosophy , aerospace engineering , operating system , continuum mechanics
Summary A return mapping algorithm in principal stress space for unified strength theory (UST) model is presented in this paper. In contrast to Mohr–Coulomb and Tresca models, UST model contains two planes and three corners in the sextant of principal stress space, and the apex is formed by the intersection of 12 corners rather than the six corners of Mohr–Coulomb in the whole principal stress space. In order to utilize UST model, the existing return mapping algorithm in principal stress space is modified. The return mapping schemes for one plane, middle corner, and apex of UST model are derived, and corresponding consistent constitutive matrices in principal stress space are constructed. Because of the flexibility of UST, the present model is not only suitable for analysis based on the traditional yield functions, such as Mohr–Coulomb, Tresca, and Mises, but might also be used for analysis based on a series of new failure criteria. The accuracy of the present model is assessed by the iso‐error maps. Three numerical examples are also given to demonstrate the capability of the present algorithm. Copyright © 2015 John Wiley & Sons, Ltd.