Anisotropic hierarchic solid finite elements for the simulation of passive-active arterial wall models

A 3D anisotropic hierarchic solid finite element formulation is provided for the passive and active mechanical response of arteries. The artery is modeled as an anisotropic nearly incompressible hyperelastic tube consisting of two layers that correspond to the media and the adventitia. These layers are considered as a fiber-reinforced material consisting of two collagen fiber families that are symmetrically disposed and helically oriented around the tube's axis. The numerical analysis is based on a 3D anisotropic hierarchic solid finite element formulation, including the possibility of varying the polynomial degree in all local directions as well as for all displacement components. For the purpose of verification, analytical solutions are provided for different benchmarks focusing on the aspects of compressible and incompressible 3D stretch, plane strain and plane stress pure shear, as well as a mono-layer anisotropic incompressible circular cylindrical artery of Holzapfel-Gasser-Ogden material under inflation and extension. The resulting solutions, including stress and strain distribution through the arterial wall, are plotted to point out the passive response and different activation levels. In addition the effect of various compressibility levels, including nearly incompressibility, is studied by numerical examples. The robustness and accuracy of the proposed method is demonstrated by comparing the results of different ansatz spaces.