Implicit integration of plasticity models for granular materials

A stress integration algorithm for granular materials based on fully implicit integration with explicit updating is presented. In the implicit method the solution makes use of the gradient to the potential surface at the final stress state which is unknown. The final stress and hardening parameters are determined solving the non-linear equations iteratively so that the stress increment fulfills the consistency condition. The integration algorithm is applicable for models depending on all the three stress invariants and it is applied to a characteristic state model for granular material. Since tensile stresses are not supported the functions and their derivatives are not representative outside the compressive octant of the principal stress space. The elastic predictor is therefore preconditioned in order to ensure that the first predictor is within the valid region. Capability and robustness of the integration algorithm are illustrated by simulating both drained and undrained triaxial tests on sand. The algorithm is developed in a standard format which can be implemented in several general purpose finite element codes. It has been implemented as an ABAQUS subroutine, and a traditional geotechnical problem of a flexible strip footing resting on a surface of sand is investigated in order to demonstrate the global accuracy and stability of the numerical solution. (C) 2003 Elsevier B.V. All rights reserved.