On Constitutive Modeling of Arteries

Abstract

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.

Predictive Continuum Constitutive Modeling of Unfilled and Filled Rubbers

“…The Treloar's experiments with all specimens taken from a single sheet of the material are usually used as a benchmark for evaluating constitutive models of incompressible isotropic hyperelastic materials [46,47,48]. The constitutive parameters of the general CSE constitutive equation in uniaxial extension mode ( 14) for Treloar's test data have numerically been solved by the trial-and-error-on-digit (TED) method and the linear least square (LLSQ) method combined by Zhao [49].…”

Modeling and Implementing Compressible Isotropic Finite Deformation without the Isochoric–Volumetric Split

“…With curve-fitting, the Poisson index of ν = 0.31041 is determined. The constitutive constants in uniaxial tension mode have been solved by the trial-and-error-on-digit (TED) method and the linear least square (LLSQ) method combined [33]. The comparison between the general CSE model and the uniaxial tension test data, along with the lateral contraction-axial stretch curve, is shown in Figure 1.…”