Accounting for the thickness effect in dynamic spherical indentation of a viscoelastic layer: Application to non-destructive testing of articular cartilage

Abstract

In recent years, dynamic indentation tests have been shown to be useful both in identification of mechanical properties of biological tissues (such as articular cartilage) and assessing their viability. We consider frictionless flat-ended and spherical sinusoidally-driven indentation tests utilizing displacement-controlled loading protocol. Articular cartilage tissue is modeled as a viscoelastic material with a time-independent Poisson's ratio. We study the dynamic indentation stiffness with the aim of formulating criteria for evaluation the quality of articular cartilage in order to be able to discriminate its degenerative state. In particular, evaluating the dynamic indentation stiffness at the turning point of the flat-ended indentation test, we introduce the so-called incomplete storage modulus. Considering the time difference between the time moments when the dynamic stiffness vanishes (contact force reaches its maximum) and the dynamic stiffness becomes infinite (indenter displacement reaches its maximum), we introduce the so-called incomplete loss angle. Analogous quantities can be introduced in the spherical sinusoidally-driven indentation test, however, to account for the thickness effect, a special approach is required. We apply an asymptotic modeling approach for analyzing and interpreting the results of the dynamic spherical indentation test in terms of the geometrical parameter of the indenter and viscoelastic characteristics of the material. Some implications to non-destructive indentation diagnostics of cartilage degeneration are discussed. (C) 2012 Elsevier Masson SAS. All rights reserved.Peer reviewe

Measurement of elastic modulus by instrumented indentation in the macro-range: Uncertainty evaluation

“…This loading range is helpful to gain a global mechanical response from high strength bulk materials and thick coatings. Indeed, the scope of our investigation is not limited to bulk materials but may be widened to layers, multilayers and coated material if the influence of the substrate on the elastic measurements and the thickness effect are properly evaluated [4][5][6][7][8]. The macro range overcomes also the indentation size effect (ISE) typical in nano/micro-IITs, i.e.…”

Articular Contact Mechanics

“…Here,δ(ω) is the so-called modified incomplete loss angle introduced by Argatov et al [11] for the viscoelastic model (see formula (7.48)). We recommend replacement of the straightforward formula (7.79) with a new relation, based on the coincidence of the corresponding modified incomplete storage moduli.…”

“…As shown in [11], the notationG n (ω) has distinct interpretations for different values of the subscript n. By changing the integration variable, the integral (7.45) may be recast in the form…”

“…Following [11], we consider the quantity 44) and note that the quantity on the right-hand side of Eq. (7.44) was previously considered in a number of studies on indentation of viscoelastic materials [49,61].…”

Linear Transversely Isotropic Biphasic Model for Articular Cartilage Layer

“…By analogy with the viscoelastic case [2,4], the quantityK 1 (ω) will be called the reduced incomplete apparent storage modulus. Substituting the expression (5.143) into the right-hand side of Eq.…”