where 𝑛 is the unit normal vector, 𝜇 𝑡 is the friction coefficient, 𝑘 𝑡 is the elastic constant for tangential contact, 𝛿 𝑛 is the overlap distance of particles i and j, 𝑆 𝑡 is the accumulated tangential displacement, 𝛾 𝑡 is the viscoelastic damping constant for tangential contact, 𝑣 𝑟 𝑡 is the tangential relative velocity of particles i and j, and 𝑡 is the unit tangential vector.