Sommario
Si discute della soluzione incrementale del problema elastoplastico con incrudimento nel campo dei grandi spostamenti (ma con piccole deformazioni intrinseche), ed in presenza di distorsioni distribuite.
Si assumono leggi costitutive del tipo associato, ammettendo la possibilità di interazione tra i modi plastici in corrispondenza dei punti singolari della superficie di snervamento.
Si dimostrano quattro proprietà di minimo della soluzione; esse riconducono il problema alla ottimizzazione di funzionali convessi (quadratici tranne che nel caso del terzo teorema) vincolata da equazioni e diseguaglianze lineari.
Si specializzano infine alcuni risultati al caso dei piccoli spostamenti e della elastoplasticità senza incrudimento.
Summary
The incremental boundary value problem for elastoplastic work-hardening continua, is discussed in the presence of large displacements but small strains, and allowing for distributed dislocations.
Associated flow laws are assumed, as is the occurrence of interaction between yielding modes in singular points of the yield surface.
Four extremum theorems are proved which reduce the problem to the optimization, under linear constraints, of convex quadratic forms (of a non linear form for the third theorem).
Finally some results are specialized to small displacements and perfectly plastic (non hardening) cases.
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This study forms part of a research programme supported by the National (Italian) Research Council (C.N.R., Gruppo Plasticità).
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De Donato, O. Some extremum theorems for the elastoplastic boundary value problem in the presence of large displacements. Meccanica 5, 210–218 (1970). https://doi.org/10.1007/BF02133577
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DOI: https://doi.org/10.1007/BF02133577