A compressible anisotropic hyperelastic model with I5 and I7 strain invariants

Abstract

It is obvious that the mechanical properties of arterial tissue include compressibility, anisotropy, and the fact that the out-of-plane shear modulus is smaller than the shear modulus in the plane of the fibers. However, the last point is rarely considered when it comes to compressible anisotropic hyperelastic models. In order to acquire different shear moduli, we propose a modified hyperelastic model including the influence of strain invariants $I_5$ and $I_7.$ The convergence and correctness of this model are verified through the hydrostatic tension test, uniaxial tension test, and shear deformation test. It turns out that our model correctly predicts an anisotropic response and volume change to hydrostatic tensile test and the fact that the out-of-plane shear modulus is always smaller than the shear modulus in the plane of the fibers in shear deformation test. We conclude that the influence of strain invariants $I_5$ and $I_7$ is great, especially in the shear deformation, so that it is necessary to include $I_5$ and $I_7$ in the compressible anisotropic hyperelastic model.

Keywords: Compressibility; anisotropy; finite element mothed; hyperelastic model.