Mathematical modeling of linear viscoelastic impact: Application to drop impact testing of articular cartilage

Abstract

In recent years, a number of experimental studies have been conducted to investigate the mechanical behavior and damage mechanisms of articular cartilage under impact loading. Some experimentally observed results have been explained using a non-linear viscoelastic impact model. At the same time, there is the need of simple mathematical models, which allow comparing experimental results obtained in drop impact testing with impact loads of different weights and incident velocities. The objective of this study was to investigate theoretically whether the main features of articular impact could be qualitatively predicted using a linear viscoelastic theory or the linear biphasic theory. In the present paper, exact analytical solutions are obtained for the main parameters of the Kelvin-Voigt and Maxwell impact models. Perturbation analysis of the impact process according to the standard viscoelastic solid model is performed. Asymptotic solutions are obtained for the drop weight impact test. The dependence of the coefficient of restitution on the impactor parameters has been studied in detail.

On application of Fung's quasi-linear viscoelastic model to modeling of impact experiment for articular cartilage

“…On the other hand, it is well known (see, e.g., [7]) that the weight of the impactor may influence the experimental results. It has been also shown in [4] that, in the case of linear Kelvin-Voigt model, the gravity effect implies that the coefficient of restitution increases with velocity for relatively high impact velocities (to be more precise for low values of the dimensionless ratio g/(ω 0 v 0 ), where g is the gravitational acceleration).…”

The two-ball bounce problem

“…[1][2][3][4][5] and references therein). This paper considers in detail a canonical impact problem, namely the impact of two balls placed vertically above one another and dropped onto a hard floor.…”

Articular Contact Mechanics

“…The coefficients a pq andâ pq are calculated by minimizing the functions 9) where N andN are the numbers of measured surface points, and (ξ…”

“…Observe that the coefficient of restitution in the linear viscoelastic impact models [9,73] depends on the impactor mass and does not depend on the impact velocity. An advantage of the Hunt-Crossley impact model is the lack of dependence of the coefficient of restitution on the mass of the colliding bodies, and thus it can be regarded as an intrinsic property of the material [73].…”

“…In the framework of the short-time contact model for thin bonded biphasic layers (see [9,14]), the corresponding equivalent instantaneous out-of-plane shear elastic modulus is 44 are the out-of-plane shear elastic moduli of the solid matrices of the biphasic layers, h 1 and h 2 are the layer thicknesses.…”