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Joined dissimilar orthotropic elastic cylindrical membranes under internal pressure and longitudinal tension

Published online by Cambridge University Press:  17 February 2009

V. G. Hart  and
Jingyu Shi
V. G. Hart
Affiliation:
Department of Mathematics, University of Queensland, Australia.
Jingyu Shi
Affiliation:
Department of Mathematics, University of Queensland, Australia.
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Abstract

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Following work in an earlier paper, the theory of finite deformation of elastic membranes is applied to the problem of two initially-circular semi-infinite cylindrical membranes of the same radius but of different material, joined longitudinally at a cross-section. The body is inflated by constant interior pressure and is also extended longitudinally. The exact solution found for an arbitrary material is now specialised to the orthotropic case, and the results are interpreted for forms of the strain-energy function introduced by Vaishnav and by How and Clarke in connection with the study of arteries. Also considered in this context is the similar problem where two semi-infinite cylindrical membranes of the same material are separated by a cuff of different material. Numerical solutions are obtained for various pressures and longitudinal extensions. It is shown that discontinuities in the circumferential stress at the joint can be reduced by suitable choice of certain coefficients in the expression defining the strain-energy function. The results obtained here thus solve the problem of static internal pressure loading in extended dissimilar thin orthotropic tubes, and may also be useful in the preliminary study of surgical implants in arteries.

Type
Research Article
Information
The ANZIAM Journal , Volume 34 , Issue 3 , January 1993 , pp. 296 - 317
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Adkins, J. E. and Rivlin, R. S., “Large elastic deformations of isotropic material, IX: the deformation of thin shells”, Phil. Trans. Roy. Soc. London A 244 (1952) 505–531.Google Scholar
[2]Bergel, D. H., “The properties of blood vessels”, in Biomechanics: Its Foundations and Objectives, (eds. Fung, Y. C., Perrone, N. & Anliker, M.) (Prentice-Hall, Englewood Cliffs, New Jersey, 1972) Chapter 5.Google Scholar
[3]Hart, V. G. and Shi, Jingyu, “Joined dissimilar isotropic elastic cylindrical membranes under internal pressure and longitudinal tension”, Quart. J. Mech. Appl. Math. 44 (1991) 581–600.CrossRefGoogle Scholar
[4]How, T. V. and Clarke, R. M., “The elastic properties of a polyurethane arterial prothesis”, J. Biomechanics 17 (1984) 597–608.CrossRefGoogle Scholar
[5]Kidson, I. G. and Abbot, W. M., “Low compliance and arterial graft occlusion”, Cardiovasc. Surg. 58 (1978) 1–1–1–3.Google ScholarPubMed
[6]Kydoniefs, A. D., “Finite axisymmetric deformations of an initially cylindrical elastic membrane enclosing a rigid body”, Q. J. Mech. Appl. Math. 22 (1969) 319–331.CrossRefGoogle Scholar
[7]Kydoniefs, A. D. and Spencer, A. J. M., “Finite axisymmetric deformations of an initially cylindrical elastic membrane”, Quart. J. Mech. Appl. Math. 22 (1969) 87–95.CrossRefGoogle Scholar
[8]Pedley, T. J., The fluid mechanics of large blood vessels, (Cambridge University Press, New York, 1980).CrossRefGoogle Scholar
[9]Pipkin, A. C., “Integration of an equation in membrane theory”, TAMP 19 (1968) 818–819.Google Scholar
[10]Rivlin, R. S. and Saunders, D. W., “Large elastic deformations of isotropic materials. VII: Experiments on the deformation of rubber”, Phil. Trans. Roy. Soc. London A 243 (1950–51) 251–288.Google Scholar
[11]Vaishnav, R. N., “Mathematical characterization of the nonlinear rheological behavior of the vascular tissue”, Biorheology 17 (1980) 219–226.Google ScholarPubMed