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

Vitucci, Gennaro; Argatov, Ivan; Mishuris, Gennady

doi:10.1002/mma.3895

Cited by 6 publications

(8 citation statements)

References 57 publications

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“…For the three-dimensional geometry described in Eq. (5), we were able to write the bones approach, the evolution of the contact area and the corresponding pressure distribution due to an arbitrary force applied onto the TITH biphasic cartilage layer treated in [43] (see Eqs. (19), (24), (29)).…”

Section: Discussionmentioning

confidence: 99%

“…Nevertheless the importance of inhomogeneity in the material property distribution across the thickness has been widely explored as a crucial factor in improving superficial fluid support, thus protecting the tissue from damage ( [18,28]). This was the reason for our recent study [43], summarized in Sec. 2, where a special exponentialtype inhomogeneity was introduced.…”

Section: Introductionmentioning

confidence: 88%

“…In the recent work [43], the deformation problem for a thin biphasic transversely isotropic, transversely homogeneous (TITH) biphasic layer was studied. An infinitely extended thin layer, firmly attached along one face, was loaded perpendicularly to the opposite one.…”

Section: Model and Statement Of The Contact Problemmentioning

confidence: 99%

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

Vitucci

Mishuris

2017

European Journal of Mechanics - A/Solids

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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.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 88%

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

Vitucci

Mishuris

2017

European Journal of Mechanics - A/Solids

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“…Recently, the problem of normal loading of a thin biphasic layer was studied by (Vitucci et al, 2016) for a special case of exponential type of non-homogeneity. The obtained asymptotic solution can be used for generalizing the asymptotic model of uniateral contact [equations (3)–(6)] for this case (Vitucci and Mishuris, 2016). …”

Section: Unsolved Problems and Directions For Future Researchmentioning

confidence: 99%

Articular Contact Mechanics from an Asymptotic Modeling Perspective: A Review

Argatov

Mishuris

2016

Front. Bioeng. Biotechnol.

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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.

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“…For instance, Lebon and Rizzoni do so by means of a two-level model with a perfect contact interface at the first level and imperfect interface at the second one [20,21,36,37]. More commonly, however, the interphase layer is represented in the model as an imperfect interface with a set of transmission conditions that simulate the physical behaviour of the original interphase [4,5,24,22,23,26,42]. Having developed this method for low-conductive curvilinear layers in [2,3], we moved on to apply a similar approach for the situation when the interphase is, contrarily, highly conductive [39].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear transmission conditions for thin highly conductive interphases of curvilinear shape

Andreeva

2018

Journal of the European Ceramic Society

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We consider heat transfer problem in a composite ceramic featuring a thin nonlinear interphase layer with distinctively different characteristics (high thermal conductivity, apart from the mentioned physical size). The presence of an interphase may be problematic for the classical FEM approach in terms of technical implementation, accuracy and stability of the results. We avoid the potential issues by replacing the interphase in the model with a zero thickness imperfect nonlinear interface with two transmission conditions. These conditions are carefully derived using asymptotic analysis and aim at preserving the physical properties of the original interphase layer now absent in the model, thus ensuring an accurate solution. Numerical examples with particular attention to various physical and geometrical aspects illustrate the validity of the described approach.

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

Cited by 6 publications

References 57 publications

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

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

Articular Contact Mechanics from an Asymptotic Modeling Perspective: A Review

Nonlinear transmission conditions for thin highly conductive interphases of curvilinear shape

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