三维FEM/DEM中摩擦力的实施及验证

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摘要块体间的相互碰撞、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。

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关键词 ：岩石力学, 三维FEM/DEM, 库仑摩擦, 势接触力, 离散元法

Abstract：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.

Key words： rock mechanics 3D FEM/DEM Coulomb friction potential contact forces discrete element method (DEM)

收稿日期: 2013-09-16

引用本文:

严成增，孙冠华，郑宏，葛修润. 三维FEM/DEM中摩擦力的实施及验证[J]. 岩石力学与工程学报, 2014, 33(6): 1248-1256.
YAN Chengzeng，SUN Guanhua，ZHENG Hong，GE Xiurun. IMPLEMENTATION AND VERIFICATION OF FRICTION IN 3D FEM/DEM. , 2014, 33(6): 1248-1256.

链接本文:

http://www.rockmech.org/CN/Y2014/V33/I6/1248

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