On the continuum formulation of higher-gradient plasticity for single and polycrystals

DOI10.1016/S0022-5096(99)00024-1zbMath0999.74029OpenAlexW2034932024MaRDI QIDQ1578524

Publication date: 2 December 2002

Published in: Journal of the Mechanics and Physics of Solids (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-5096(99)00024-1

zbMATH Keywords

single crystals polycrystals kinematic hardening yield condition continuum theory of dislocations fourth-order spatial derivatives of plastic strain geometrically linear formulation higher-gradient plasticity nonlocal evolution law second-order spatial derivatives of plastic deformation gradient

Mathematics Subject Classification ID

Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity) (74C10) Crystalline structure (74E15) Statistical mechanics of crystals (82D25)

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Cites Work