Abstract The Hertzian contact model is prominent for characterizing the contact behaviors of particles in three dimensions (3D), while its two-dimensional (2D) version in the tangential direction has not been well-established yet. In this work, a semianalytical Hertzian frictional contact model in 2D is developed, with an analytical solution for the normal contact behavior and a semianalytical solution with a variable penalty factor for the tangential contact behavior. Numerical analyses with finite element simulations are performed to characterize the penalty factor and validate the proposed contact model. The results show that the penalty factor increases with the contact width and Poisson’s ratio based on which an empirical equation of the penalty factor is provided. Using the penalty factor calculated from the empirical equation, the contact behaviors evaluated from the proposed contact model match fairly well with those of finite element simulations. The proposed contact model is implemented in a discrete element code. Quantitative analyses of a bi-axial compression test on polydispersed particles demonstrate the stability and effectiveness of the proposed contact model. The proposed contact model could be useful to the computational mechanics of particles in 2D and parallel-axis cylinders with strip contacts in 3D.

中文翻译：

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二维半解析赫兹摩擦接触模型

摘要 Hertzian 接触模型在表征粒子在三维 (3D) 中的接触行为方面很突出，而其在切线方向上的二维 (2D) 版本尚未完善。在这项工作中，开发了二维半解析赫兹摩擦接触模型，其中包含法向接触行为的解析解和切向接触行为具有可变惩罚因子的半解析解。使用有限元模拟进行数值分析以表征惩罚因子并验证所提出的接触模型。结果表明，惩罚因子随着接触宽度和泊松比的增加而增加，并在此基础上提供了惩罚因子的经验方程。使用从经验方程计算的惩罚因子，从建议的接触模型评估的接触行为与有限元模拟的接触行为非常匹配。建议的接触模型是在离散元素代码中实现的。对多分散颗粒的双轴压缩试验的定量分析证明了所提出的接触模型的稳定性和有效性。所提出的接触模型可用于 2D 中的粒子和 3D 中带条接触的平行轴圆柱体的计算力学。