Isaac Scientific Publishing

Journal of Advances in Applied Mathematics

On Constitutive Modeling of Arteries

Download PDF (7940.4 KB) PP. 54 - 68 Pub. Date: April 1, 2019

DOI: 10.22606/jaam.2019.42003


  • Fuzhang Zhao
    APD Optima Study, Lake Forest, CA 92630, USA


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.


Arteries, constitutive modeling, experimental tests, magic angle, TED-LLSQ method.


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