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Journal of Advances in Applied Mathematics
JAAM > Volume 4, Number 2, April 2019

On Constitutive Modeling of Arteries

Download PDF  (7940.4 KB)PP. 54-68,  Pub. Date:March 1, 2019
DOI: 10.22606/jaam.2019.42003

Author(s)
Fuzhang Zhao
Affiliation(s)
APD Optima Study, Lake Forest, CA 92630, USA
Abstract
The magic angle of θm = arctan[(p5 + 1)/2]  58.2825°, rather than  θ = arccos(1/ p3)  54.7356°, has been discovered through theoretical derivations for arteries to accommodate twist buckling optimally. The magic angle matches many published experimental results by others. As byproducts of the derivation, the stable deformation ranges for normal and shear stretches are defined. The anisotropic continuum stored energy (CSE) functional has been used to model the equibiaxial tension tests of porcine thoracic aortas and special simple normal tests of human abdominal aorta aneurysms. In CSE models, constitutive constants are determined by a trial-and-error-on-digit (TED) method and the linear least squares (LLSQ) method combined.
Keywords
Arteries, constitutive modeling, experimental tests, magic angle, TED-LLSQ method.
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