Comparison of explicit and implicit integration schemes for the Barcelona Basic Model

The paper presents a comparison between a range of explicit and implicit stress integration schemes applied to the Barcelona Basic Model (BBM). The implicit algorithms tested are a general and an optimised return mapping algorithm for BBM. The latter is characterized by analytical integration of the hardening law and by solving only a single non-linear equation. This improves the stability and accuracy of the stress integration and reduces the required computing time. The explicit algorithms assessed include three Runge-Kutta algorithms with adaptive substepping and local error control and an extrapolation algorithm with substepping and global error control. A comparison of the algorithms accuracy and assessment of stability is presented based on tests with three sets of BBM material parameters and strain increments covering the range from zero to three percent of volumetric and shear strain.