Rolling and sliding between non-spherical particles

Besides normal and tangential forces, rolling and sliding are also important interactions of particles, and should be considered in the discrete element method. However, there are various definitions of rolling and sliding, some of which are quite different and even contradictory. On the premise of trying not to use definitions, the rolling and sliding velocities between non-spherical particles are derived, and satisfy the objectivity. The sliding and rolling velocities between spherical particles are included in the results as a special case. A rolling resistance model calculated by the rolling velocity is applied to simulate direct shear tests of non-spherical particles. In addition to coinciding with experiments, the shear curves also satisfy the rate independent theory. As a demonstration of the model's universality, the wave propagation in uniaxial compression tests is also simulated.