Force propagation speed in a bed of particles due to an incident particle impact

The force propagation speed in granular matter is a very difficult property to be measured. A new technique has been developed to calculate the force propagation speed in granular matter based on measuring experimentally the contact time. The contact time for a particle hitting a bed of particles is estimated as the time taken for a particle to strike a bed of particles till the time of its ejection, and it is calculated using the discrete element method. The speed of force propagation in a bed of particles is estimated by plotting the dependence of the path length of the contact force on the contact time and finding the gradient of such dependence. Such approach leads to accurate results if the impact speed is below the yield velocity, i.e. no plastic deformations. It is found that the force propagation speed in spherical granular matter is proportional to the impact speed of the incident particle, which is different from force propagation in continuum matter. It is also found that the propagation speed is dependent on the material and diameters ratio of the interacting particles, but it is not dependent on the number of bed layers. The propagation speed in granular matter is normalized by dividing it by a reference propagation speed, i.e. the propagation speed at an impact speed of 1 m/s. It is found that the normalized propagation speed is independent of the material and diameter of the interacting particles, but it is logarithmically proportional to the impact speed. The proportionality constant is equal to 0.16, which can be taken as a universal constant for force propagation in spherical granular matter.