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中文摘要：
块体问的相互碰撞、滑移均涉及到摩擦力的问题，但原有的三维有限元／离散元（FEM／DEM）并未考虑摩擦力的作用，为解决这一问题，首先论述三维FEM／DEM中基于势的接触力，指出势是对嵌入及接触所存储能量的表征，势越大表示嵌入量越大，接触所存储的能量越大。然后，在原有三维FEM／DEM中加入经典的库仑摩擦，使得原有三维FEM／DEM可以考虑摩擦力。最后，通过有解析解的斜面滑块算例和拱桥垮塌算例验证实施库仑摩擦的正确性，结果表明斜面滑块算例的数值解与解析解很好地吻合；而拱桥垮塌算例表明FEM／DEM可以解决复杂的工程问题。
英文摘要：
Collision and slide between blocks are related to friction, while the original three-dimensional combined finite-discrete element method（FEM/DEM） did not consider the effect of friction. The FEM/DEM based on the potential associated with contact force was therefore discussed in detail. The potential was found to characterize the stored energy due to embedding and contacts; namely, the greater the potential, the greater the embedding and the energy stored in the contact. The classic Coulomb friction was then taken into account in the original three-dimensional FEM/DEM. An example of slider-on-ramp having an analytical solution and an example of bridge collapsing were analysed, which verified the correctness of implementation of Coulomb friction. The results show that the numerical solution of the example of bevel slider is in good agreement with the analytical solution and the improved FEM/DEM is capable of solving complex engineering problems.
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