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Efficient return algorithms for associated plasticity with multiple yield planes
Author(s) -
Clausen J.,
Damkilde L.,
Andersen L.
Publication year - 2005
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.1595
Subject(s) - discontinuity (linguistics) , infinitesimal , mathematics , yield (engineering) , plane (geometry) , mathematical analysis , geometry , materials science , composite material
A new return method for implicit integration of linear isotropic yield criteria is presented. The basic idea is to perform all the manipulations in the principal stress space and thereby achieve very simple formulae for calculating the plastic corrector stresses, based on the constant gradient of such criteria. The return formulae are in closed form and no iteration is required. The method accounts for three types of stress return: return to a single yield plane, to a discontinuity line at the intersection of two yield planes and to a discontinuity point at the intersection between three or more yield planes. The infinitesimal and the consistent elastoplastic constitutive matrix are calculated for each type of stress return, as are the conditions to ascertain which type of return is required. The method is exemplified with the Mohr–Coulomb yield criterion. Copyright © 2005 John Wiley & Sons, Ltd.