基于能量守恒的球单元离散元法向接触力计算方法

An Energy-conserving Calculation Method of Normal Contact Force for Discrete Element Method(DEM)of Ball Element based on Spherical Particles

接触力计算模型是DEM的重要环节,现有的法向接触力计算模型中,对延性材料的模拟结果较好,但对脆性材料误差较大。经典离散元理论中的Cundall系列模型并未考虑单元形状对接触力的影响,Hertz模型虽计算结果较为准确,但条件要求严苛,很难直接推广至其他形状。本文建立了一种基于能量守恒的法向接触力计算模型—体积模型,以势能函数为基础,推导出球形单元法向接触力的计算公式;同时独立开发完整的离散元算法程序框架,将模型嵌入到离散元程序中;设计混凝土球形颗粒试验,将试验结果与模拟结果对比,结果表明体积模型在脆性材料的法向接触力计算中有更高精度。

The contact force calculation model is an important part of DEM.In the existing normal contact force calculation model, the simulation results of ductile materials are better, but the error of brittle materials is larger.The Cundall series model in the classical discrete element theory does not consider the influence of the element shape on the contact force.Although the Hertz model has accurate calculation results, it is difficult to directly extend to other shapes due to the strict requirements.In this paper, a calculation model-volume model of normal contact force based on energy conservation is established, and the calculation formula of normal contact force of spherical element is derived based on the potential energy function;at the same time, the complete discrete element algorithm program framework is independently developed, and the model is embedded into the discrete element program;the experiment of concrete spherical particles is designed, and the experimental results are compared with the simulation results.The results show that the volume model has higher accuracy in the calculation of normal contact force of brittle materials.