A mathematical analysis for indentation tests of articular cartilage.

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

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A mathematical analysis for indentation tests of articular cartilage.

Journal Article•DOI•

A mathematical analysis for indentation tests of articular cartilage.

Wilson C. Hayes¹, Leon M. Keer¹, G. Herrmann¹, Lyle F. Mockros¹•Institutions (1)

Northwestern University¹

01 Sep 1972-Journal of Biomechanics (Elsevier)-Vol. 5, Iss: 5, pp 541-551

TL;DR: Solutions for the indentation of the layer by the plane end of a rigid circular cylinder and by a rigid sphere are suggested as useful for the determination of the elastic shear modulus of intact cartilage.

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About: This article is published in Journal of Biomechanics.The article was published on 1972-09-01. It has received 899 citations till now. The article focuses on the topics: Indentation.

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Skeletal Tissue Mechanics

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TL;DR: This poster presents a probabilistic procedure for estimating the mechanical properties of bone based on known mechanisms, including compressive forces, compressive strength, and the compressive properties of Bone.

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Journal Article•DOI•

Determination of elastic moduli of thin layers of soft material using the atomic force microscope.

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Emilios K. Dimitriadis¹, Ferenc Horkay¹, Julia A. Maresca¹, Bechara Kachar¹, Richard S. Chadwick¹ - Show less +1 more•Institutions (1)

National Institutes of Health¹

01 May 2002-Biophysical Journal

TL;DR: It is shown that the use of sharp cantilever tips, which typically induce local strains that far exceed the linear material regime, can be alleviated by using microspheres as probes, and the criteria for their use is established.

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Journal Article•DOI•

Fluid transport and mechanical properties of articular cartilage: A review

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Van C. Mow¹, Mark H. Holmes¹, W. M. Lai¹•Institutions (1)

Rensselaer Polytechnic Institute¹

01 Jan 1984-Journal of Biomechanics

TL;DR: This review is aimed at unifying the understanding of cartilage viscoelastic properties in compression, in particular the role of compression-dependent permeability in controlling interstitial fluid flow and its contribution to the observed vis coelastic effects.

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1,000 citations

Journal Article•DOI•

Biphasic indentation of articular cartilage--II. A numerical algorithm and an experimental study.

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Van C. Mow¹, M.C. Gibbs², W. M. Lai¹, Wenbo Zhu¹, Kyriacos A. Athanasiou¹ - Show less +1 more•Institutions (2)

Columbia University¹, Albany Medical College²

01 Jan 1989-Journal of Biomechanics

TL;DR: An efficient numerical algorithm is developed to compute all three material coefficients of cartilage in situ on the joint surface from the indentation creep experiment, and the average values of the aggregate modulus are determined.

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561 citations

Cites background or methods from "A mathematical analysis for indenta..."

...In the Parsons and Black studies (1977) the authors showed the ‘internal consistency’ of the Hayes et al. (1972) elasticity theory with the experimental data by plotting the calculated values of the ‘geometric scaling function rc(a/h, v)’ against the area-aspect ratio a/h for v = 0....
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...$ In addition, the mathematical solutions for the indentation problem used by most of these investigators were those derived by Hertz (1882) and Hayes et al. (1972), which further...
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...$ In addition, the mathematical solutions for the indentation problem used by most of these investigators were those derived by Hertz (1882) and Hayes et al. (1972), which further assumed the conditions of infinitesimal strain and frictionless indenter tip....
[...]
...In the Parsons and Black studies (1977) the authors showed the ‘internal consistency’ of the Hayes et al. (1972) elasticity theory with the experimental data by plotting the calculated values of the ‘geometric scaling function rc(a/h, v)’ against the area-aspect ratio a/h for v = 0.4. This value was also assumed by Hoch et al. (1983) in their study of biomechanical and biochemical changes in rabbit tibia1 plateau cartilage even though values as high as 0....
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...A][ &-$I. (12) Values of K were numerically tabulated by Hayes et al. (1972) for six values of Poisson’s ratio from 0.3 to 0.5 and 15 values of a/h from 0.2 to 8....
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Journal Article•DOI•

Biphasic indentation of articular cartilage--I. Theoretical analysis.

[...]

Arthur F.T. Mak, W. M. Lai¹, Van C. Mow¹•Institutions (1)

Columbia University¹

01 Jan 1987-Journal of Biomechanics

TL;DR: A mathematical solution has been obtained for the indentation creep and stress-relaxation behavior of articular cartilage where the tissue is modeled as a layer of linear KLM biphasic material of thickness h bonded to an impervious, rigid bony substrate.

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490 citations

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References

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Journal Article•DOI•

The frictional properties of animal joints

[...]

C.W. McCutchen¹•Institutions (1)

University of Cambridge¹

01 Jan 1962-Wear

TL;DR: A series of friction experiments were performed which provide confirmation that animal joints are weeping bearings and confirm that synovial fluid is an excellent lubricant for cartilage.

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575 citations

Journal Article•DOI•

Viscoelastic properties of human articular cartilage.

[...]

W C Hayes, L F Mockros

01 Oct 1971-Journal of Applied Physiology

291 citations

Journal Article•DOI•

The determination of a creep modulus for articular cartilage from indentation tests on the human femoral head

[...]

G.E. Kempson¹, M.A.R. Freeman¹, S.A.V. Swanson¹•Institutions (1)

Imperial College London¹

01 Jul 1971-Journal of Biomechanics

TL;DR: The method takes into account the limited and variable thickness of cartilage and permits variations in cartilage stiffness on the femoral head, as measured by the creep modulus, to be recorded.

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198 citations

Journal Article•DOI•

Tensile Properties of Articular Cartilage

[...]

Geoffrey Edward Kempson¹, M. A. R. Freeman¹, S. A. V. Swanson¹•Institutions (1)

University of London¹

14 Dec 1968-Nature

TL;DR: Electron microscopy studies show that the collagen fibres near the articular surface are predominantly parallel to the surface; viewed perpendicularly to thesurface, they also show a dominant orientation which varies systematically over the whole joint surface.

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Abstract: ARTICULAR cartilage consists principally of collagen fibres embedded in a mucopolysaccharide ground substance. Electron microscopy studies1 show that the collagen fibres near the articular surface are predominantly parallel to the surface; viewed perpendicularly to the surface, they also show a dominant orientation which varies systematically over the whole joint surface. In contrast, the fibres in the deeper zones have a more random distribution with a tendency to be perpendicular to the surface. The fibre diameter and distance between adjacent fibres appear to increase with depth from the articular surface. Chemical and physico-chemical studies (unpublished results of H. Muir and A. Maroudas) confirm that the collagen density decreases with depth from the articular surface.

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168 citations

Journal Article•DOI•

Axisymmetric contact problem for an elastic layer

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N. N. Lebedev, Ia.S. Ufliand

01 Jan 1958-Journal of Applied Mathematics and Mechanics

TL;DR: In this paper, the problem of pressing a stamp of circular cross-section into an elastic layer was solved by expressing the required displacements and stresses in terms of one auxiliary function, which represented the solution of a Fredholm integral equation with a continuous symmetrical kernel.

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118 citations