3D mode discrete element method: Elastic model

For block systems that satisfy small strain, finite displacement, and finite rotation conditions, a three-dimensional mode-deformable discrete element method (3MDEM) is presented. The 3MDEM is an efficient numerical method that simulates the mechanical behavior of nonlinear, large deformation, and dynamic problems. Under the assumption of small strain, the motion of points in a deformable block can be decomposed into the sum of the block's rigid body motion and the deformation of the block itself. The kinematic equations for deformable blocks are derived. The deformation of blocks can be expressed by the combination of a series of deformation modes, which can be decoupled under given orthogonal conditions. The results of the simulation verify that good accuracy can be obtained under the small strain condition using the presented method, compared with the finite element method. Under the condition of finite deformation, reasonably similar results are obtained by the proposed method and a commercial three-dimensional deformable distinct element code, 3DEC. In the case of verification examples, the 3MDEM is found to be more efficient than 3DEC.