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

Abstract

Fully implicit integration schemes have been demonstrated to be very robust and efficient for nonlinear elastoplastic and elastic–viscoplastic models and enjoy widespread use in finite element formulations. The paper introduces a new form of fully implicit local and global algorithms for the integration of nonlinear elastoplastic constitutive laws including anisotropic plasticity and hysteretic small strain elastic nonlinearity. The local stress integration algorithm is based on a single step backward differentiation method with iterative solution for the predictor as well as the corrector steps. The global system of implicit nonlinear equations is solved with a quasi-Newton technique using a numerical tangent computed every load step by finite difference and optimized with iterative updating using the Broyden–Fletcher–Goldfarb–Shano (BFGS) procedure. The proposed numerical procedure is illustrated here through the implementation of a set of nonlinear constitutive equations describing the response of lightly overconsolidated cohesive materials. Numerical simulations of single element tests as well as a boundary value problem confirm the robustness, accuracy, and efficiency of the proposed algorithm at the local and global level.