Deep learning-accelerated multiscale approach for granular material modeling

The hierarchical finite element method (FEM)-discrete element method (DEM) multiscale approach is a powerful tool for solving geotechnical boundary value problems. However, despite parallel computing can be resorted to, the high computational cost remains an insurmountable barrier to its practical application in engineering-scale problems. As an alternative, a deep learning model (DLM) is employed to replace the representative volume element (RVE) in the DEM. The complex constitutive responses of sand under various loading paths can be reproduced by leveraging the powerful learning capacity of the DLM. During the numerical computations, the DLM is integrated into the Gauss integration points of the FEM mesh, where it receives strains as input and returns the prediction of stresses to advance the calculation. The applicability and accuracy of the approach were examined with three BVPs, in which the sources of error for both global and local performances were systematically analyzed. The feasibility of the approach in accounting for the inherent anisotropy of sand was also investigated. The results demonstrated that the incorporation of the DLM can achieve a significant computational acceleration of up to two orders of magnitude while maintaining a high degree of accuracy.