Finite element implementation of non-linear elastoplastic constitutive
laws using local and global explicit algorithms with automatic error
control
International Journal for Numerical Methods in Engineering, 50 (5):
1191-1212 (2001)DOI: 10.1002/1097-0207(20010220)50:5
Abstract
Implicit stress integration algorithms have been demonstrated to provide
a robust formulation for finite element analyses in computational
mechanics, but are difficult and impractical to apply to increasingly
complex non-linear constitutive laws. This paper discusses the performance
of fully explicit local and global algorithms with automatic error
control used to integrate general non-linear constitutive laws into
a non-linear finite element computer code. The local explicit stress
integration procedure falls under the category of return mapping
algorithm with standard operator split and does not require the determination
of initial yield or the use of any form of stress adjustment to prevent
drift from the yield surface. The global equations are solved using
an explicit load stepping with automatic error control algorithm
in which the convergence criterion is used to compute automatically
the coarse load increment size. The proposed numerical procedure
is illustrated here through the implementation of a set of elastoplastic
constitutive relations including isotropic and kinematic hardening
as well as small strain hysteretic non-linearity. A series of numerical
simulations confirm the robustness, accuracy and efficiency of the
algorithms at the local and global level. Published in 2001 by John
Wiley & Sons, Ltd.