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A linear algebra approach to stress and strain at a point and theories of yield
Author(s) -
Milner P. R.
Publication year - 1992
Publication title -
strain
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.477
H-Index - 47
eISSN - 1475-1305
pISSN - 0039-2103
DOI - 10.1111/j.1475-1305.1992.tb00781.x
Subject(s) - yield surface , von mises yield criterion , yield (engineering) , mathematics , algebra over a field , matrix (chemical analysis) , shear stress , stress (linguistics) , linear algebra , point (geometry) , shear (geology) , structural engineering , pure mathematics , geometry , engineering , materials science , finite element method , physics , mechanics , constitutive equation , metallurgy , composite material , linguistics , philosophy
A straightforward method is described whereby the magnitudes and directions of the principal stresses and strains in two or three dimensions may be derived using the matrix methods of elementary linear ulgebra. The ideas are extended to simplify the classical derivation of the extreme values of shear stress and of the octahedral stresses. After a description of several visual aids, the work concludes with a definition of the von Mises yield surface consistent with the foregoing procedures.