Nanomanipulation of elliptic and cubic nanoparticles with consideration of the impact theories

Viscoelastic Hertzian Impact

“…Moreover, the characteristic relaxation time 1/η is assumed to be much larger than the impact duration, that is, ηt c ≪ 1 or, which is asymptotically the same, ηt 0 c ≪ 1. The analytical approximations are given in terms of the small dimensionless parameter ε, which, in view of (1) and (24), is proportional to ηt 0 c , where t 0 c is the Hertzian impact duration (see Equations ( 1) and (7) 2 ). Namely, Hertz's theory of impact yields the following characteristic time:…”

“…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].…”

Experimental extraction of Young's modulus of gastric tissue with development of spherical, cylindrical, and crowned rollers contact theories

“…Also, considering the approximate relation of the Hunter impact, the effects of the impact on motion are also considered. Finally, the results are calculated after 3 s under constant, linear, second-order and Sin forces for elliptical and cubic nanoparticles [ 22 ].…”