A Lagrangian coupling approach for the combination of finite-discrete element method

In this paper, an effective approach to couple finite elements (FEs) with discrete elements (DEs) is presented. The proposed approach conforms to displacement compatibility condition at the interface between FEs and DEs, and this constraint is enforced by the Lagrange multiplier method. The coupling system is solved by the Gauss-Seidel iteration strategy and the incompatibility of degrees of freedom between FEs and DEs can be effectively addressed. Two numerical examples are employed for validation and the effectiveness of the proposed approach is also demonstrated via comparison with other numerical methods.