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The Theory of Scalar Plastic Deformation Functions
Author(s) -
Rees D. W. A.
Publication year - 1983
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19830630602
Subject(s) - bauschinger effect , torsion (gastropod) , isotropy , hardening (computing) , plastic bending , plasticity , strain hardening exponent , anisotropy , mathematics , classical mechanics , mathematical analysis , materials science , geometry , physics , composite material , optics , bending , medicine , surgery , bending stiffness , layer (electronics)
Starting with the assumption of initial isotropy and the kinematic hardening rule the anisotropic nature of plastic deformation in polycrystalline materials is expressed through functions of two deformation scalars which in themselves are polynomial functions of the seven independent invariants of the deviatoric stress and plastic strain tensors. These former functions are shown to represent closely the translation, contraction, rotation and distortion that has been observed in experimental yield loci under combined tension and torsion. A physical interpretation is presented for the case of a linear workhardening material displaying a Bauschinger effect and an absence of cross‐hardening at the limit of proportionality.