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      Extension of Small-Strain Theory to Finite Deformation of Cylindrical Vessels by Internal Over-Pressure

      Journal of Vascular Research

      S. Karger AG

      Pressure distention, Elastic cylinders, Infinitesimal theory, Lengthening isotropic vessels

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          Abstract

          Calculations of the pressure distention of closed cylindrical vessels using classical infinitesimal-strain theory predict that, for isotropic materials, the length remains fixed while the diameter increases linearly with pressure. These predictions can be verified experimentally only if the radial deformation is less than 2–3%. This paper develops formulae applicable to deformations up to approximately 10 times the above, based on a modification of infinitesimal theory. The results predict significant lengthening of isotropic vessels, and ballooning or ‘blow-out’ above a certain pressure. It is shown that the classical stresses contain a common hydrostatic component which must be subtracted before the stresses can be integrated across the wall thickness to yield wall tensions. When the hydrostatic component is taken into account, Laplace’s law is found to hold for thick-walled vessels as well as for thin-walled vessels.

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          Author and article information

          Journal
          JVR
          J Vasc Res
          10.1159/issn.1018-1172
          Journal of Vascular Research
          S. Karger AG
          1018-1172
          1423-0135
          1970
          1970
          18 September 2008
          : 7
          : 5
          : 257-272
          Affiliations
          Institute of Respiratory Physiology, Virginia Mason Research Center, Seattle, Wash, and the Department of Physiology and Biophysics, University of Washington, Seattle, Wash.
          Article
          157841 Angiologica 1970;7:257–272
          10.1159/000157841
          © 1970 S. Karger AG, Basel

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          Page count
          Pages: 16
          Categories
          Paper

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