On Constitutive Modeling of Arteries

The magic angle of θm = arctan[( √ 5 + 1)/2] ≈ 58.2825 • , rather than θ = arccos(1/ √ 3) ≈ 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.