An implicit integration algorithm for the finite element implementation ofa nonlinear anisotropic material model including hysteretic nonlinearity

Fully implicit integration schemes have been demonstrated to be very robust and efficient for nonlinear elastoplastic and elastic-viscoplastic viscopl astic models and enjoy widespread use in finite element Formulations. The p aper introduces a new form of fully implicit local and global algorithms fo r the integration of nonlinear elastoplastic constitutive laws including an isotropic plasticity and hysteretic small strain elastic nonlinearity. The local stress integration algorithm is based on a single step backward diffe rentiation method with iterative solution for the predictor as well as the corrector steps. The global system of implicit nonlinear equations is solve d with a quasi-Newton technique using a numerical tangent computed every lo ad step by finite difference and optimized with iterative updating using th e Broyden-Fletcher-Goldfarb-Shano (BFGS) procedure. The proposed numerical procedure is illustrated here through the implementation of a set of nonlin ear constitutive equations describing the response of lightly overconsolida ted cohesive materials. Numerical simulations of single element tests as we ll as 3 boundary value problem confirm the robustness. accuracy, and effici ency of the proposed algorithm at the local and global level. (C) 2000 Else vier Science B.V. All rights reserved.