Coefficient of restitution for one-dimensional harmonic solids

Impact of composite soft-rigid elastic projectiles: A numerical study

We study by numerical simulation the impact of a one-dimensional composite projectile, composed of two superposed homogeneous parts, on an infinitely rigid and massive wall. The coefficient of restitution and the contact time are systematically measured as functions of the contrasts of mass and stiffness between the two parts. For purely elastic parts, these quantities show complex trends associated with different dynamics of the deformation waves propagating inside the projectile. A significant portion of the initial kinetic energy can be trapped in the deformation modes: the coefficient of restitution is lowest, about 0.2, when there is a strong stiffness contrast between the two parts and the stiff and soft parts are at the leading and trailing edges of the projectile respectively. In this case, we highlight the presence of multiple bounces, whose number increases as the proportion of the soft part increases. Finally, viscoelastic parts can be implemented in the same numerical framework to successfully recover the results obtained in real composite projectile impact experiments [D'Angelo et al., Phys. Rev. E 103, 053005 (2021)2470-004510.1103/PhysRevE.103.053005].

Impact dynamics of composite elastorigid projectiles onto solid surfaces

We investigate the impact of composite objects. They consist of a soft layer on top of a rigid part with a hemispherical impacting end. The coefficient of restitution (e) of such objects is studied systematically as a function of the mass ratio and of the nature of the materials. For rather elastic materials, the coefficient of restitution is a nonmonotonic function of the mass ratio and exhibits important variations. The dynamics of the impact can be characterized by several bounces depending on the ratios between the four timescales at play. These include the duration of contact of the rigid part with the substrate and the time for the elastic waves to travel back and forth in the soft layer. In that sense, describing these projectiles requires one to take into account both the Hertzian theory of contact and the elastic waves described by Saint-Venant's approach.

Passage of a monomer through a nonrigid periodical substrate formed by noninteracting particles

The paper examines a classical system in one degree of freedom: a particle (monomer) interacting with a periodic lattice of independent, separated oscillators. The monomer can interact with oscillators via a short-range attractive potential force. The periodic lattice of oscillators may absorb the energy of the monomer launched at some initial velocity, but it does so in a very peculiar manner. The monomer velocity gradually decreases, approaching near some nonzero limit value. The limiting monomer velocities can assume discrete values only. This behavior of the monomer is accounted for by the existing resistance force that completely vanishes at certain monomer velocities.

Collision of one-dimensional nonlinear chains

We investigate one-dimensional collisions of unharmonic chains and a rigid wall. We find that the coefficient of restitution (COR) is strongly dependent on the velocity of colliding chains and has a minimum value at a certain velocity. The relationship between COR and collision velocity is derived for low-velocity collisions using perturbation methods. We found that the velocity dependence is characterized by the exponent of the lowest unharmonic term of interparticle potential energy.

Trapping, reflection, and fragmentation in a classical model of atom-lattice collisions

A classical one-dimensional model of the collision of an atom of mass M with a cold, semi-infinite harmonic lattice comprised of identical atoms of mass m is considered. In the model, the interactions between the incident atom (adatom) and the lattice are described in terms of a truncated parabolic potential by which the adatom is harmonically bound to the lattice at short distances but evolves freely when its distance is larger than a critical length R(c). The dynamics of the adatom colliding with an infinitely cold lattice is studied as a function of the initial velocity of the adatom. In order to determine whether the colliding atom is bound or reflected from the lattice in the asymptotic time limit, "secondary" collision events in which the incident atom leaves and reenters the interaction zone of the lattice are carefully considered. It is demonstrated that secondary collisions anticipated to be important for heavy adatoms (mu=m/M<1) also occur in the case of light adatoms (mu > or = 1). It is shown that the neglect of secondary collisions leads to an underestimation of the lower energy bound for adatom reflection of roughly 10% for mu close to 1. By generalizing the model to allow for the breaking of lattice bonds, the phenomenon of collision-induced lattice fragmentation is investigated.

Stochastic dynamics with a mesoscopic bath

We consider the effects of bath size on the nature of the dynamics and transport properties for two simple models in which the bath is composed of a collinear chain of harmonic oscillators. The first model consists of an untwisted rotating chain (elastic rotor) for which we obtain a non-Markovian equation analogous to the generalized Langevin equation for the rotational degrees of freedom. We demonstrate that the corresponding memory function oscillates with a frequency close to that of the lowest mode of the chain. The second model considered consists of a tagged oscillator in a finite harmonic chain. For this model, we find an additional harmonic force in the generalized Langevin equation for the terminal atom that does not appear in the equation of motion for the semi-infinite chain. It is demonstrated that the force constant for the additional harmonic force scales as 1/N, where N is the number of oscillators in the chain. Using an exact representation for the velocity correlation function, the transport properties of the model are discussed.