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Spherical indentation of a membrane on an elastic half-space

Published online by Cambridge University Press:  31 January 2011

Jae Hun Kim  and
Andrew Gouldstone
Jae Hun Kim
Affiliation:
Department of Materials Science and Engineering, SUNY Stony Brook, Stony Brook, New York 11794-2275
Andrew Gouldstone*
Affiliation:
Department of Materials Science and Engineering, SUNY Stony Brook, Stony Brook, New York 11794-2275
*
a)Address all correspondence to this author. e-mail: [email protected]
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Abstract

A number of physiological systems involve contact or indentation of solids with tensed surface layers. In this paper the contact problem of spherical indentation of a linear elastic solid, covered with a tensed membrane is addressed. Semianalytical solutions are obtained relating indentation force to contact radius, as well as contact radius to depth. Good agreement is found between derived equations and results from finite element method (FEM) simulations. In addition, effect of membrane on subsurface stresses is shown quantitatively and compared favorably to FEM results. This work is applicable to mechanical property assessment of a number of biological systems.

Keywords

BiomaterialElastic properties
Type
Articles
Information
Journal of Materials Research , Volume 23 , Issue 8 , August 2008 , pp. 2212 - 2220
Copyright
Copyright © Materials Research Society 2008

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References

REFERENCES

1Szilard, R.: Theory and Analysis of Plates: Classical and Numerical Methods Prentice-Hall Englewood Cliffs, NJ 1973Google Scholar
2Zamir, E.A.Taber, L.A.: On the effects of residual stress in microindentation tests of soft tissue structures. J. Biomech. Eng.—Trans. ASME 126, 276 2004CrossRefGoogle ScholarPubMed
3Lai-Fook, S.J., Wilson, T.A., Hyatt, R.E.Rodarte, J.R.: Elastic-constants of inflated lobes of dog lungs. J. Appl. Physiol. 40, 508 1976CrossRefGoogle ScholarPubMed
4Hajji, M.A.: Indentation of a membrane on an elastic half space. J. Appl. Mech.—Trans. ASME 45, 320 1978CrossRefGoogle Scholar
5Gouldstone, A., Brown, R.E., Butler, J.P.Loring, S.H.: Stiffness of the pleural surface of the chest wall is similar to that of the lung. J. Appl. Physiol. 95, 2345 2003CrossRefGoogle ScholarPubMed
6Sneddon, I.N.: The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47 1965CrossRefGoogle Scholar
7Hertz, H.: Ueber die beruehrung fester elastische Koerper (On the contact of elastic solids). Journal fur die reine und angewandte Mathematik 92, 156 1882Google Scholar
8Yang, W.H.Hsu, K.H.: Indentation of a circular membrane. J. Appl. Mech.—Trans. ASME 38, 227 1971CrossRefGoogle Scholar
9Timoshenko, S.Goodier, J.N.: Theory of Elasticity 3rd ed.McGraw-Hill New York, NY 1969Google Scholar
10Hajji, M.A.: Indentation of a membrane on an elastic half space with application to material testing of inflated lung lobesPh.D. Thesis, University of Minnesota, 1978CrossRefGoogle Scholar
11Ugural, A.C.: Stresses in Plates and Shells 2nd ed.McGraw Hill Boston, MA 1999Google Scholar
12ABAQUS Theory manual, version 6.2 Hibbitt, Karlsson, and Sorensen Inc. Pawtucket, RI 2001Google Scholar
13Stamenovic, D.: Mechanical-properties of pleural membrane. J. Appl. Physiol. 57, 1189 1984CrossRefGoogle ScholarPubMed
14Johnson, K.L.: Contact Mechanics Cambridge University Press New York, NY 1985CrossRefGoogle Scholar