Chapter 18 - Three-Dimensional Mode Discrete Element Method: Elastic Model

Abstract

A three-dimensional mode-deformable discrete element method (3MDEM) is presented for block systems that satisfy small strain, finite displacement and finite rotation conditions. This efficient numerical method 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. Kinematic equations for deformable blocks are derived. Deformation of blocks can be expressed by a series of deformation modes, which can be decoupled under given orthogonal conditions. The simulation results verify that good accuracy is achievable under the small strain condition using this method, compared with the finite element method. Under the condition of finite deformation, similar results are obtained by the proposed method and a three-dimensional deformable distinct element code, 3DEC. In verification examples, 3MDEM is more efficient than 3DEC.