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Classical plasticity and viscoplasticity models reformulated: theoretical basis and numerical implementation
Author(s) -
Ibrahimbegović Adnan,
Gharzeddine Fadi,
Chorfi Lotfi
Publication year - 1998
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19980830)42:8<1499::aid-nme443>3.0.co;2-x
Subject(s) - viscoplasticity , plasticity , state variable , finite element method , mathematics , computation , operator (biology) , dissipation , compressibility , basis (linear algebra) , mathematical optimization , constitutive equation , geometry , mechanics , algorithm , structural engineering , physics , engineering , biochemistry , chemistry , repressor , gene , transcription factor , thermodynamics
The well‐known phenomenological model of small strain rate‐independent plasticity is reformulated in this paper. The main difference from the classical expositions concerns the absence of the plastic strain from the list of state variables. We show that with the proposed choice of state variables, including the total and the elastic strains and strain‐like variables which control hardening, we recover all the ingredients of the classical model from a minimum number of hypotheses: instantaneous elastic response and the principle of maximum plastic dissipation. We also show that using a regularized, penalty‐like form of the principle of maximum plastic dissipation, we can recover the classical viscoplasticity model. As opposed to the previous schemes used for the finite element implementation of this model (e.g. B ‐ bar method), we propose an approach in which the basic set of equations need not be modified. The operator split method is used to simplify the details of the numerical implementation concerning both the computation of state variables and the incompatible mode based finite element approximations. The latter proves to be indispensable for accommodating the near‐incompressible deformation patterns arising in the classical plasticity. An extensive set of numerical simulations is used to illustrate the proposed formulation. © 1998 John Wiley & Sons, Ltd.