Approximate coefficient of restitution for nonlinear viscoelastic contact with external load

Abstract

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Viscoelastic Hertzian Impact

“…Recent interest in viscoelastic impact arose in modeling such diverse phenomena as dynamic response of biological soft tissues [4], hopping of a rover on an asteroid [5], fruit drop tests [6], impact of nanomanipulation of nanoparticles [7], kinetic energy dissipation in granular matter [8], seismic pounding [9], erosion [10], and protective performance of flexible polymer material [11]. It goes without saying that the case of linearly viscoelastic materials is a base case for more elaborate time-dependent material models such as poroviscoelasticity [12] and surface viscoelasticity [13].…”

“…It should be emphasized that, in contrast with the Hunt-Crossley model (8), where the current contact reaction depends only on the current kinematic variables w(t) and ẇ(t), in the viscoelastic Hertzian contact, a preceding history of loading is important. This allows for gaining insight into the hereditary effect in a bouncing impact [47], whereas the Hunt-Crossley reaction element forgets about the prior loading as soon as it returns into the intact state (i.e., w(t) = 0).…”

“…Why do we need to study the viscoelastic Hertzian impact then? If the material behavior follows a linearly viscoelastic constitutive law, the dissipative contact model (8) still can be applied for describing a spherical impact, but the model parameters χ and β should be initialized from the impact itself (indeed, χ and β are not material parameters). On the other hand, when the impact model has been derived using the solution of the viscoelastic Hertzian contact problem, the viscoelastic material parameters that enter the contact reaction model can be determined from an independent material deformation test.…”

Experimental study of the restitution coefficient of spherical particles

“…Therefore, the fundamental issue related to the macroscopic mechanical properties of particle systems lies in understanding the changes in the restitution coefficient. This change is influenced by several factors such as the shape of the particles, their material composition, density, and collision velocity [3][4]. The concept of the restitution coefficient is introduced to quantify the velocity changes that occur before and after a collision, ensuring IOP Publishing doi:10.1088/1742-6596/2730/1/012008 2 accuracy in describing these interactions.…”