Open AccessON THE DECOMPOSITION OF STRESS AND STRAIN TENSORS INTO SPHERICAL AND DEVIATORIC PARTS
Author(s) -
Giuliano Augusti,
Jussi Martin,
William Prager
Publication year - 1969
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.63.2.239
Subject(s) - isotropy , transverse isotropy , compressibility , anisotropy , stress (linguistics) , elasticity (physics) , work (physics) , decomposition , stress–strain curve , classical mechanics , materials science , mechanics , physics , deformation (meteorology) , composite material , thermodynamics , chemistry , optics , organic chemistry , linguistics , philosophy
It is well known that Hooke's law for a linearly elastic, isotropic solid may be written in the form of two relations that involve only the spherical or only the deviatoric parts of the tensors of stress and strain. The example of the linearly elastic, transversely isotropic solid is used to show that this decomposition is not, in general, feasible for linearly elastic, anisotropic solids. The discussion is extended to a large class of work-hardening rigid, plastic solids, and it is shown that the considered decomposition can only be achieved for the incompressible solids of this class.