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A linearized integration technique for incremental constitutive equations
Author(s) -
Bardet J. P.,
Choucair W.
Publication year - 1991
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.1610150102
Subject(s) - constitutive equation , geomechanics , stress path , mathematics , boundary value problem , von mises yield criterion , torsion (gastropod) , uniqueness , ordinary differential equation , finite element method , mathematical analysis , structural engineering , differential equation , geotechnical engineering , engineering , cauchy stress tensor , medicine , surgery
A numerical technique is proposed to obtain stress–strain response curves from rate‐type and incremental constitutive equations during generalized loadings. The proposed method linearizes the loading constraints of laboratory experiments, links them to the constitutive relations, and forms a linear system of ordinary differential equations. It circumvents the difficulties associated with the non‐uniqueness and bifurcation of boundary value problems. The method is illustrated for the elastoplastic von Mises and Roscoe and Burland models subjected to torsion, circular stress path, and undrained triaxial compression. The approach pertains to most stress–strain relationships and laboratory experiments of geomechanics. It is useful for research on material modelling, engineering practice and computational mechanics.