An investigation of nonlinear tangential contact behaviour of a spherical particle under varying loading

An analytical and numerical study of the tangential contact of a spherical particle under varying combined normal-tangential loading is presented. The normal and tangential contact is described by the Hertz and regularized Coulomb laws. This study is focused on the analysis of the tangential displacement of the particle’s contact point under variable normal force and reevaluation of the procedures for calculation of the tangential force. The incremental displacement-driven and force-driven constitutive relationships are developed. The importance of an adequate numerical treatment of the tangential component of the contact force is shown for the slide mode, and the recommendations for its evaluation are proposed. The performance of the algorithm is demonstrated by solving the problem of the oblique impact of the spherical particle on the wall. The suggested methodology allows us to analyse the elastic and sliding effects of the tangential interaction more precisely than existing methodologies. Besides, the issue of the direction of the tangential force, when the Coulomb limit is reached, was reconsidered in one-dimensional case by taking three versions of the unit direction vector, which are based on the tangential elastic displacement, tangential stick force, and tangential relative velocity of the contact point of the particle.