3D distinct element method

For block systems with small strain,finite displacement and finite rotation,a 3-dimensional mode distinct element method(3MDEM) was presented.It was an efficient numerical method for simulating mechanical behaviors of block systems including nonlinear,large deformation and dynamic problems.First,the motion and deformation equations of blocks were derived.Second,under the small deformation condition,the motion of deformable blocks could be decomposed into rigid body motion and deformation.Third,based on several deformation modes,the deformation of blocks could be expressed by the combination of deformation modes,which could be decoupled under the specific conditions.The blocks were not need to be discretized in 3MDEM.So regarding the deformation simulation of blocks,3MDEM was more efficient than 3DEM.It was shown that the displacements and stresses obtained by 3MDEM was coherence with those obtained by FEM under the condition of small deformation.Under the large deformation condition,the simulation results of structures by 3MDEM agreed well with those by 3DEM,and appeared with a good numerical stability.