Analysis of the Unilateral Contact Problem for Biphasic Cartilage Layers With an Elliptic Contact Zone and Accounting for Tangential Displacements

European Journal of Mechanics - A/Solids

2017

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Inhomogeneity and anisotropy play a crucial role in attributing articular cartilage its properties. The frictionless contact model constructed here consists in two thin biphasic transversely isotropic transversely homogeneous (TITH) cartilage layers firmly attached onto rigid substrates and shaped as elliptic paraboloids of different radii. Using asymptotic techniques, a solution to the deformation problem of such material has been recently obtained extending previous ones referred to homogeneous materials. The layer itself is thin in comparison with the size of the contact area and the observed time is shorter than the hydrogel characteristic time. The emerging three-dimensional contact problem is solved in closed-form and numerical benchmarks for constant and oscillating loads are given. The results are shown in terms of contact pressure and approach of the bones. The latter is derived to be directly proportional to the contact area. Existing experimental data are reinterpreted in view of the current model formulation. Comparisons are made with existing solutions for homogeneous biphasic materials in order to underline the functional importance of inhomogeneity in spreading the contact pressure distribution across the contact area. Particular attention is paid to the applicability of the retrieved formulas for interpreting measurements of in vivo experiments. Future directions are also prospected.

Section: Model and Statement Of The Contact Problemmentioning

confidence: 99%

Three-dimensional contact of transversely isotropic transversely homogeneous cartilage layers: A closed-form solution

Vitucci

European Journal of Mechanics - A/Solids

2017

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“…The refined condition takes into account the tangential displacements, which undergo the contacting points during the contact deformation, thereby increasing the complexity of the contact problem in the non-axisymmetric case (Rogosin et al, 2016) and introducing a certain correction into the solution (namely, the relation between the contact force and the contact approach turns out to be most susceptible to the effect of tangential displacements).…”

Section: Asymptotic Modeling Of Articular Contactmentioning

confidence: 99%

Articular Contact Mechanics from an Asymptotic Modeling Perspective: A Review

Argatov

Front. Bioeng. Biotechnol.

2016

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In the present paper, we review the current state-of-the-art in asymptotic modeling of articular contact. Particular attention has been given to the knee joint contact mechanics with a special emphasis on implications drawn from the asymptotic models, including average characteristics for articular cartilage layer. By listing a number of complicating effects such as transverse anisotropy, non-homogeneity, variable thickness, nonlinear deformations, shear loading, and bone deformation, which may be accounted for by asymptotic modeling, some unsolved problems and directions for future research are also discussed.

Unilateral Frictionless Contact of Thin Bonded Incompressible Elastic Layers

Argatov

Advanced Structured Materials

2015

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This chapter is devoted to solving contact problems for thin bonded incompressible transversely isotropic elastic layers in the thin-layer approximation, based on the leading-order asymptotic model developed in Chap. 2. Asymptotic Model for the Frictionless Contact of Thin Bonded Incompressible LayersIn this section we summarize the results of the asymptotic analysis performed in Sects. 2.5 and 2.7, by formulating a leading-order asymptotic model to describe (in the thin-layer approximation) the frictionless contact interaction of two incompressible elastic layers bonded to rigid substrates. Leading-Order Asymptotic Model for the Unilateral ContactWe will continue use of previous notation, wherever possible, and consider two thin transversally isotropic elastic layers of uniform thicknesses h 1 and h 2 ideally bonded to rigid substrates (see Fig. 3.1). Let ϕ(y) and δ 0 denote the gap between the layer surfaces before deformation and the contact approach of the rigid substrates under the external normal load, respectively.