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On the modelling of non‐linear kinematic hardening at finite strains with application to springback—Comparison of time integration algorithms
Author(s) -
Vladimirov Ivaylo N.,
Pietryga Michael P.,
Reese Stefanie
Publication year - 2007
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/nme.2234
Subject(s) - kinematics , isotropy , strain hardening exponent , hardening (computing) , exponential function , finite volume method , finite element method , euler's formula , mathematics , computer science , algorithm , structural engineering , mathematical analysis , mechanics , engineering , materials science , classical mechanics , physics , quantum mechanics , layer (electronics) , composite material
The paper discusses the derivation and the numerical implementation of a finite strain material model for non‐linear kinematic and isotropic hardening. The kinematic hardening component represents a continuum extension of the classical rheological model of Armstrong–Frederick kinematic hardening. In addition, a comparison between several numerical algorithms for the integration of the evolution equations is conducted. In particular, a new form of the exponential map that preserves the plastic volume and the symmetry of the internal variables, as well as two modifications of the backward Euler scheme are discussed. Finally, the applicability of the model for springback prediction is demonstrated by performing simulations of the draw‐bending process and a comparison with experiments. The results show an excellent agreement between simulation and experiment. Copyright © 2007 John Wiley & Sons, Ltd.