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Consistent tangent matrices for density‐dependent finite plasticity models
Author(s) -
PérezFoguet Agustí,
RodríguezFerran Antonio,
Huerta Antonio
Publication year - 2001
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.165
Subject(s) - tangent , tangent stiffness matrix , plasticity , mathematics , multiplicative function , isotropy , matrix (chemical analysis) , mathematical analysis , exponential function , quadratic equation , convergence (economics) , tangent space , finite element method , geometry , stiffness matrix , materials science , physics , quantum mechanics , thermodynamics , economics , composite material , economic growth
The consistent tangent matrix for density‐dependent plastic models within the theory of isotropic multiplicative hyperelastoplasticity is presented here. Plastic equations expressed as general functions of the Kirchhoff stresses and density are considered. They include the Cauchy‐based plastic models as a particular case. The standard exponential return‐mapping algorithm is applied, with the density playing the role of a fixed parameter during the nonlinear plastic corrector problem. The consistent tangent matrix has the same structure as in the usual density‐independent plastic models. A simple additional term takes into account the influence of the density on the plastic corrector problem. Quadratic convergence results are shown for several representative examples involving geomaterial and powder constitutive models. Copyright © 2001 John Wiley & Sons, Ltd.