An improved integral non-linear model for the contact of particles in distinct element simulations

Abstract

In this paper we consider a non-linear model for the elastic-frictional contact of spherical particles based on a modification of the classical Hertz–Mindlin no-slip solution. The characteristics of the original model are described and discussed in terms of the capabilities to simulate collisions using the distinct element method (DEM). Perfectly elastic collisions in normal direction and elastic-frictional mechanisms in tangential direction are considered for impacts of a sphere with a flat wall at various angles. On this basis, we suggest a mathematical modification of Mindlin's tangential solution and demonstrate formally its advantages with respect to the commonly used model. We illustrate a comparison of the proposed model with other commonly used models and a validation of the models against experimental data, available under similar conditions (Kharaz et al., Powder Technology 120 (2001) 281). It is shown that an improved realism and consistency is obtained with our modification, especially regarding the tangential displacement and force–displacement relation, at the cost of a very simple modification of the model algorithm.