Concurrent multiscale method is a spatial and temporal combination of two different scale models for describing the micro/meso and macro mixed behaviors observed in strain localization, failure and phase transformation processes, etc. Most of the existing coupling schemes use the displacement compatibility conditions to glue different scale models, which leads to displacement continuity and stress discontinuity for the obtained multiscale model. To overcome stress discontinuity, this paper presented a multiscale method based on the generalized bridging domain method for coupling the discrete element (DE) and finite element (FE) models. This coupling scheme adopted displacement and stress mixed compatibility conditions. Displacements that were interpolated from FE nodes were prescribed on the artificial boundary of DE model, while stresses at numerical integration points that were extracted from DE contact forces were applied on the material transition zone of FE model (the coupling domain and the artificial boundary of FE model). In addition, this paper proposed an explicit multiple time-steps integration algorithm and adopted Cundall nonviscous damping for quasi-static problems. DE and FE parameters were calibrated by DE simulations of a biaxial compression test and a deposition process. Numerical examples for a 2D cone penetration test (CPT) show that the proposed multiscale method captures both mesoscopic and macroscopic behaviors such as sand soil particle rearrangement, stress concentration near the cone tip, shear dilation, penetration resistance vibration and particle rotation, etc, during the cone penetration process. The proposed multiscale method is versatile for maintaining stress continuity in coupling different scale models.
Keywords: Stress continuity, Multiscale method, Discrete element method, Finite element method, Cone penetration test