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Continuous Distribution of Dislocations and the Mathematical Theory of Plasticity
Author(s) -
Mura T.
Publication year - 1965
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220100205
Subject(s) - plasticity , curvature , dislocation , von mises yield criterion , isotropy , prandtl number , strain rate , materials science , classical mechanics , yield (engineering) , mathematical analysis , mathematics , mechanics , physics , geometry , thermodynamics , composite material , optics , finite element method , heat transfer
Mises' yield criterion, the Prandtl‐Reuss relation between stress and plastic strain rate, and Hencky's theorem on shear lines for isotropic elastic‐plastic materials are derived from the theory of continuous distributions of dislocations. A linear relation between the velocity of dislocations and the gliding force acting on the dislocations is assumed in the derivation. Within this framework, the constant k in Mises' yield criterion and the scalar factor μ* in the Prandtl‐Reuss relation can be interpreted in the light of dislocation behavior. It can be also proved that the plastic curvature rate disappears and the curvature rate of the material equals the elastic curvature rate of the lattices.