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Limits to the Jaumann stress rate
Author(s) -
Molenkamp F.
Publication year - 1986
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.1610100205
Subject(s) - rotation (mathematics) , polar decomposition , stress (linguistics) , granular material , principal stress , mechanics , polar , subroutine , polar coordinate system , classical mechanics , mathematics , materials science , physics , composite material , geometry , computer science , shear stress , linguistics , philosophy , astronomy , operating system
Abstract In this paper it is shown that the Jaumann stress rate is not accurate for moderate deformations with deviatoric strains of more than 10 per cent; in such cases the objective stress rate is better calculated using the material rotation rate as calculated by polar decomposition. For very large deformations of granular materials this approach becomes invalid too because then the fabric tends to rotate together with principal stresses. Apparently in general the fabric rotation of a granular material cannot be described by continuum mechanics alone. For the numerical calculation of the material rotation for moderate deformations a numerical subroutine, based on polar decomposition, has been developed.