Large Deformation Analysis of the Arterial Cross Section

[+] Author and Article Information
B. R. Simon, A. S. Kobayashi

Department of Mechanical Engineering, University of Washington, Seattle, Wash.

D. E. Strandness

Department of Surgery, University of Washington, Seattle, Wash.

C. A. Wiederhielm

Department of Physiology and Biophysics, University of Washington, Seattle, Wash.

J. Basic Eng 93(2), 138-145 (Jun 01, 1971) (8 pages) doi:10.1115/1.3425199 History: Received August 18, 1970; Online October 27, 2010


Possible relations between arterial wall stresses and deformations and mechanisms contributing to atherosclerosis are discussed. Necessary material properties are determined experimentally and from available data in the literature by assuming the arterial response to be a static finite deformation of a thick-walled cylinder constrained in a state of plane strain and composed of an incompressible, nonlinear elastic, transversely isotropic material. Experimental justification from the literature and supporting theoretical considerations are presented for each assumption. The partial derivative of the strain energy density function δW1 /δI , necessary for in-plane stress calculation, is determined to be of exponential form using in situ biaxial test results from the canine abdominal aorta. An axisymmetric numerical integration solution is developed and used as a check for finite element results. The large deformation finite element theory of Oden is modified to include aortic material nonlinearity and directional properties and is used for a structural analysis of the aortic cross section. Results of this investigation are: (a) Fung’s exponential form for the strain energy density function of soft tissues is found to be valid for the aorta in the biaxial states considered; (b) finite deformation analyses by the finite element method and numerical integration solution reveal that significant tangential stress gradients are present in arteries commonly assumed to be “thin-walled” tubes using linear theory.

Copyright © 1971 by ASME
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