Axisymmetric contact problem for a biphasic cartilage layer with allowance for tangential displacements on the contact surface

Argatov, Ivan; Mishuris, Gennady

doi:10.1016/j.euromechsol.2010.07.003

Cited by 14 publications

(24 citation statements)

References 24 publications

(42 reference statements)

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“…In this study we extend results obtained in papers [4] and [5] by considering the influence of the tangential displacements on the contact problem for cartilage layers with the contact zone of elliptic shape based on the biphasic material model. Note that the perturbation method proposed in [7] could be one of the options for the analysis, however, the procedure is too complex to perform even a few asymptotic steps.…”

Section: Introductionmentioning

confidence: 83%

“…It was shown in [8] (see also [4]) that vertical and the tangential displacements of each bone can be represented in the form…”

Section: Formulation Of the Contact Problemmentioning

confidence: 99%

“…In particular, it was shown [4] that accounting for the tangential displacements is important in the case of diseased cartilage where the measurement of indentation depth may differ even as much as 10% in comparison with the healthy case. In [5], the unilateral contact problem for articular cartilages bonded to subchondral bones with a contact zone in the shape of an arbitrary ellipse has been considered, and a closed form analytic solution was found.…”

Section: Introductionmentioning

confidence: 99%

“…Note that the perturbation method proposed in [7] could be one of the options for the analysis, however, the procedure is too complex to perform even a few asymptotic steps. Here, employing some technique and ideas from [4] and [5], we propose another way to construct the asymptotics which utilises the assumption that the shape of the contact zone is an ellipse at the initial stage of deformation and can be regarded as a small perturbation of the ellipse at any other stage of deformation.…”

Section: Introductionmentioning

confidence: 99%

“…An asymptotic modeling approach to study the contact problem for biphasic cartilage layers has been performed by Argatov and Mishuris in a series of articles (see [4,5,7]). In particular, it was shown [4] that accounting for the tangential displacements is important in the case of diseased cartilage where the measurement of indentation depth may differ even as much as 10% in comparison with the healthy case.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Rogosin

Mishuris

Koroleva

et al. 2016

Mathematical Modelling and Analysis

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A three-dimensional unilateral contact problem for articular cartilage layers attached to subchondral bones shaped as elliptic paraboloids is considered in the framework of the biphasic cartilage model. The main novelty of the study is in accounting not only for the normal (vertical), but also for tangential vertical (horisontal) displacements of the contacting surfaces. Exact general relationships have been established between the contact approach and some integral characteristics of the contact pressure, including the contact force. Asymptotic representations for the contact pressure integral characteristics are obtained in terms of the contact approach and some integral characteristics of the contact zone. The main result is represented by the first-order approximation problem.

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Section: Introductionmentioning

confidence: 83%

“…It was shown in [8] (see also [4]) that vertical and the tangential displacements of each bone can be represented in the form…”

Section: Formulation Of the Contact Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Rogosin

Mishuris

Koroleva

et al. 2016

Mathematical Modelling and Analysis

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An asymptotic model for the deformation of a transversely isotropic, transversely homogeneous biphasic cartilage layer

Vitucci

Argatov

Mishuris

2016

Math Methods in App Sciences

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a Communicated by I. SevostianovIn the present paper, an asymptotic model is constructed for the short-time deformation of an articular cartilage layer modeled as transversely isotropic, transversely homogeneous biphasic material. It is assumed that the layer thickness is relatively small compared with the characteristic size of the normal surface load applied to the upper surface of the cartilage layer, while the bottom surface is assumed to be firmly attached to a rigid impermeable substrate. In view of applications to articular contact problems, it is assumed that the interstitial fluid is not allowed to escape through the articular surface.

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Deformation of a Thin Bonded Transversely Isotropic Elastic Layer

Argatov¹,

Mishuris²

2015

Advanced Structured Materials

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In this chapter we study frictionless contact problems for a thin transversely isotropic elastic layer bonded to a rigid substrate and indented by a smooth absolutely rigid punch under the assumption that the layer thickness is relatively small compared to the characteristic size of the contact area. We apply a perturbation technique to obtain asymptotic solutions of different degrees of accuracy and formulate simple mathematical models (called asymptotic models) to describe the deformational behavior of a bonded compressible elastic layer in the thin-layer approximation. In particular, the effects of unilateral contact interaction (with a priori unknown contact area) and the tangential displacements at the contact interface (taken into account in formulating the contact condition) are considered. It is shown that the case of an incompressible layer requires special consideration.

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Axisymmetric contact problem for a biphasic cartilage layer with allowance for tangential displacements on the contact surface

Cited by 14 publications

References 24 publications

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

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

An asymptotic model for the deformation of a transversely isotropic, transversely homogeneous biphasic cartilage layer

Deformation of a Thin Bonded Transversely Isotropic Elastic Layer

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