Finite element implementation of non-linear elastoplastic constitutive laws using local and global explicit algorithms with automatic error control

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-line ar constitutive laws. This paper discusses the performance of fully explici t local and global algorithms with automatic error control used to integrat e general non-linear constitutive laws into a non-linear finite element com puter 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 s tress adjustment to prevent drift from the yield surface. The global equati ons are solved using an explicit load stepping with automatic error control algorithm in which the convergence criterion is used to compute automatica lly the coarse load increment size. The proposed numerical procedure is ill ustrated here through the implementation of a set of elastoplastic constitu tive 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.