A Lagrange multiplier-based coupling approach for the combined finite-discrete element method applicable to mechanical investigation of composite materials

The discrete element (DE) method is advantageous in modelling fracture behaviour because of its particle characteristics, but it is computationally costly. The finite element (FE) method is efficient in computation, but it might encounter some issues in modelling large deformation problems and fracture. The motivation of this work is to combine the both methods that uses DE particles in the region of particular interest and FE meshes in the remaining regions to save computation time. The key to this combined finite-discrete element method is the employment of an effective coupling approach. In this work, an approach based on Lagrange multiplier method is proposed to couple a FE domain with a DE domain at the interface. The different number of the degree of freedoms between each FE node and each DE particle is naturally taken into account by the governing equations and this incompatibility issue is addressed by incorporating rotational effect into the displacement compatibility condition. The displacement compatibility condition is enforced by the Lagrange multiplier method, and no material overlapping is allowed between different subdomains. A number of numerical examples are employed for validation and good agreement with the results from other numerical methods is observed. Numerical results confirm the effectiveness of the Lagrange multiplier-based coupling approach for both similar and dissimilar materials.