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Implicit integration of elastoplastic relations with reference to soils
Author(s) -
Runesson Kenneth
Publication year - 1987
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.1610110308
Subject(s) - dilatant , plasticity , mathematics , isotropy , yield surface , elasticity (physics) , constitutive equation , projection (relational algebra) , flow (mathematics) , mathematical analysis , mechanics , geotechnical engineering , geometry , geology , finite element method , physics , thermodynamics , algorithm , quantum mechanics
The stress solution in plasticity with an associated or a non‐associated flow rule is considered. Upon fully implicit integration of the relevant constitutive relations the stress is obtained as the projection of the (fictitious) elastic stress onto the yield surface for given values of the hardening softening variables. This projection is defined, for a general non‐associated flow rule, in adjusted complementary elastic energy, which becomes exactly the complementary energy when the flow rule is associated. Isotropic elasticity and mean‐stress dependent isotropic yield criteria (pertinent to soil) are considered and the implications of a certain class of non‐associated flow rules are evaluated. This class relates to dilatant (or contractant) materials and involves non‐associated plastic volume change. The corresponding stress solutions are shown to be strongly influenced by Poisson's ratio and by the dilation angle.