Coefficient of restitution for elastic disks

2009

Phys. Rev. E

Impact phenomena of nanoclusters subject to thermal fluctuations are numerically investigated. From the molecular dynamics simulation for colliding two identical clusters, it is found that the restitution coefficient for head-on collisions has a peak at a colliding speed due to the competition between the cohesive interaction and the repulsive interaction of colliding clusters. Some aspects of the collisions can be understood by the theory by Brilliantov et al. (Phys. Rev. E 76, 051302 (2007)), but many new aspects are found from the simulation. In particular, we find that there are some anomalous rebounds in which the restitution coefficient is larger than unity. The phase diagrams of rebound processes against impact speed and the cohesive parameter can be understood by a simple phenomenology.

Section: Introductionmentioning

confidence: 99%

Simulation of cohesive head-on collisions of thermally activated nanoclusters

2009

Phys. Rev. E

“…For high velocity of the impact they demonstrate the macroscopic deformation has left after the collision is over. Although it is not easy to discuss the impact with the very low impact velocity from their method, their analysis may suggest the possibility of a complicated relation between the quasi-static theory of impact 14,15,16 and their microscopic simulation 18 . Thus, we have to clarify the relation between two typical approaches.…”

Section: Introductionmentioning

confidence: 99%

The Impact of Two-Dimensional Elastic Disk

2001

J. Phys. Soc. Jpn.

The impact of a two-dimensional elastic disk with a wall is numerically studied. It is clarified that the coefficient of restitution (COR) decreases with the impact velocity. The result is not consistent with the recent quasi-static theory of inelastic collisions even for very slow impact. The abrupt drop of COR has been found due to the plastic deformation of the disk, which is assisted by the initial internal motion. (to be published in

“…We should note that the strong repulsion F(l (i) s ) is introduced to inhibit the penetration of the disk to the surface of the wall [5]. Thus, the dynamical equation of motion for each mass point i of the lower half boundary of the disk is described by…”

mentioning

confidence: 99%

Anomalous Behavior of the Coefficient of Normal Restitution in Oblique Impact

2004

Phys. Rev. Lett.

The coefficient of normal restitution in an oblique impact is theoretically studied. Using a twodimensional lattice model for an elastic disk and an elastic wall, we demonstrate that the coefficient of normal restitution can exceed unity and has a peak against the incident angle in our simulation. We also explain this behavior based upon a phenomenological theory.The coefficient of normal restitution e is introduced to determine the normal component of the post-collisional velocity in the collision of two materials. The coefficient e is defined bywhere v(τ ) is the relative velocity of the centers of mass of two colliding materials at time τ measured from the initial contact, τ c is the duration of a collision, and n is the unit vector normal to the contact plane. Though some text books of elementary physics state that e is a material constant, many experiments and simulations show that e decreases with increasing impact velocity [1]. The dependence of e on the low impact velocity is theoretically treated by the quasi-static theory [2,3,4]. We also recognize that e can be less than unity for the normal impact without the introduction of any explicit dissipation, because the macroscopic inelasticities originate in the transfer of the energy from the translational mode to the internal modes such as the vibrations [3,5,6]. While e has been believed to be less than unity in most situations, it is recently reported that e can exceed unity in oblique impacts [7,8,9]. In particular, Louge and Adams [9] observed oblique impacts of a hard aluminum oxide sphere on a thick elastoplastic polycarbonate plate and found that e grows monotonically with the magnitude of the tangent of the incident angle γ. In their experiment, Young's modulus of the plate is 100 times smaller than that of the aluminum oxide sphere. They also suggested that e can exceed unity for the most oblique impacts.In this letter, we demonstrate that our twodimensional simulation of the oblique impact based on Hamilton's equation has yielded an increasing e with tan γ and e exceeds unity at the critical incident angle. Finally, we explain our results by our phenomenological theory.Let us introduce our numerical model [10]. Our model consists of an elastic disk and an elastic wall (Fig. 1). The width and the height of the wall are 8R and 2R, respectively, where R is the mean radius of the undeformed disk. The both side ends and the bottom of the wall are fixed. We place 800 mass points at random in a disk with the radius R and 4000 mass points at random in a wall for the disk and the wall, respectively. We connect each mass point with its neighbor mass points by the Delaunay triangulation algorithm [11], and undeformed nonlinear springs are placed on all the connections.Each mass point i on the lower half boundary of the disk feels the force,is the distance between i-th surface mass point of the disk and the nearest surface spring of the wall, a = 300/R, V 0 = amc 2 R/2, m is the mass of each mass point, c is the one-dimensional velocity of sound, and n (i) ...