A mathematical analysis for indentation tests of articular cartilage

W. C. Hayes; Leon M Keer; G. Herrmann; L. F. Mockros

doi:10.1016/0021-9290(72)90010-3

A mathematical analysis for indentation tests of articular cartilage

W. C. Hayes^*, Leon M Keer, G. Herrmann, L. F. Mockros

^*Corresponding author for this work

Civil and Environmental Engineering

Research output: Contribution to journal › Article › peer-review

757 Scopus citations

Abstract

A mathematical model is developed for indentation tests of articular cartilage. The cartilage, normally bonded to the subchondral bone, is modeled as an infinite elastic layer bonded to a rigid half space, and the indenter is assumed to be a rigid axisymmetric punch. The problem is formulated as a mixed boundary value problem of the theory of elasticity and solutions are obtained for the indentation of the layer by the plane end of a rigid circular cylinder and by a rigid sphere. Subject to detailed verification with independent tests, the present solutions are suggested as useful for the determination of the elastic shear modulus of intact cartilage.

Original language	English (US)
Pages (from-to)	541-551
Number of pages	11
Journal	Journal of Biomechanics
Volume	5
Issue number	5
DOIs	https://doi.org/10.1016/0021-9290(72)90010-3
State	Published - Jan 1 1972

ASJC Scopus subject areas

Biophysics
Orthopedics and Sports Medicine
Biomedical Engineering
Rehabilitation

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N2 - A mathematical model is developed for indentation tests of articular cartilage. The cartilage, normally bonded to the subchondral bone, is modeled as an infinite elastic layer bonded to a rigid half space, and the indenter is assumed to be a rigid axisymmetric punch. The problem is formulated as a mixed boundary value problem of the theory of elasticity and solutions are obtained for the indentation of the layer by the plane end of a rigid circular cylinder and by a rigid sphere. Subject to detailed verification with independent tests, the present solutions are suggested as useful for the determination of the elastic shear modulus of intact cartilage.

AB - A mathematical model is developed for indentation tests of articular cartilage. The cartilage, normally bonded to the subchondral bone, is modeled as an infinite elastic layer bonded to a rigid half space, and the indenter is assumed to be a rigid axisymmetric punch. The problem is formulated as a mixed boundary value problem of the theory of elasticity and solutions are obtained for the indentation of the layer by the plane end of a rigid circular cylinder and by a rigid sphere. Subject to detailed verification with independent tests, the present solutions are suggested as useful for the determination of the elastic shear modulus of intact cartilage.

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A mathematical analysis for indentation tests of articular cartilage

Abstract

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