Study on Impact of Equivalent Two Bodies : Coefficients of Restitution of Spheres of Brass, Lead, Glass, Porcelain and Agate, and the Material Properties

Discrete and continuum descriptions of shaken granular matter

“…These particular are in accordance with previous experimental measurements [129,117]. The use of a velocity-dependent r 0 ensures that dissipation is not over-estimated at high particle densities, as can occur when using constant coefficients [130].…”

“…The explicit form of the collision law is given in the Appendix. These particular values are known to reproduce complex behaviour observed in similar vibrated setups using stainless-steel spheres ofd = 1 mm tod = 5 mm in diameter [56,42], and where picked based on previous experimental measurements [117]. In order to avoid inelastic collapse we use the TC model [87], with a constant value t c = 10 −6 (d/g) 1/2 , withd the (dimensional) diameter of the spheres, andg the (dimensional) gravity.…”

“…We disregard rotational degrees of freedom, and any other physical effect that is not captured by the hard-sphere model, with the goal of keeping the model as simple as possible. This particular value is in accordance with collisions of glass or stainless steel particles [117]. In order to avoid inelastic collapse, the TC model is used, where particle collisions are considered elastic if they occur within a given time, which we take as t c = 10 −5 [87].…”

Moderately high speed impact of two identical spheres

“…They are simple and stable but the maximum impact velocity is mainly limited by the arm length. So, they are commonly used in the range of impact velocity up to 3 m/s [6,7,12,13,16]. To produce higher impact velocity, an air gun setup which can produce the impact speed of 10e20 m/s was used in this study.…”

“…Tatara [4] and Villaggio [5] developed extensive theories to the impact of elastic sphere. Goldsimth [6] and Tatara [7] performed experiments and presented various relations between the coefficient of restitution and impact velocity. L. Vu-Quoc et al [8] developed a force-deformation model involving plastic deformation.…”