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中文摘要：
本文针对小应变、大位移和大转动的块体系统建立了三维模态变形体离散元数值模型（3MDEM）。首先推导了包含块体刚体运动和变形的整体运动和变形方程,同时提出了在小变形条件下,变形块体的运动可以分解为块体刚体运动和变形的叠加,从而分别推导出刚体平移、转动和变形的方程,并用变形模态分解块体的变形模式。和一般的离散元方法相同,本文模型也采用了显式的时步步进求解格式,适用于求解非连续、大变形及动力问题。该模型克服了三维变形体离散元（3DEM）需要对块体内部细分网格导致计算量急剧上升的缺点,具有高效、仿真和可变形的特点。一系列算例表明：本文模型在小变形以及连续介质力学领域可以给出和有限元相媲美的应力和位移结果,而在大变形、大位移的强非线性领域可以给出与3DEM相媲美的计算结果,并具有良好的数值稳定性。
英文摘要：
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.
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