A semianalytical Hertzian frictional contact model in 2D

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. (c) 2020 Elsevier Inc. All rights reserved.

Automated summary

The study developed a semi-analytical Hertzian frictional contact model in 2D to characterize the contact behaviors of particles in the tangential direction. Numerical analyses and validation with finite element simulations demonstrated the accuracy and stability of the proposed contact model. The results provided an empirical equation for the penalty factor, showing that it increases with the contact width and Poisson's ratio, leading to a good match between the proposed model and finite element simulations.