Mathematical Modeling of Anisotropic Hyperelastic Cylindrical Thick Shells by Incorporating Thickness Deformation and Compressibility with Application to Arterial Walls

Abstract

This paper is devoted to mathematical modeling of anisotropic hyperelastic thick cylindrical shells like arteries by taking into account the volume compressibility and through-the-thickness deformation. To describe the hyperelastic behavior of this kind of shells and extract their constitutive relations, the modified anisotropic (MA) model is employed, which is able to characterize compressible behavior of hyperelastic materials like soft tissues. By considering the arterial segment as a thick cylindrical shell, the higher order thickness deformation shell theory together with nonlinear Green’s strains are exploited to express its deformations and capture the thickness stretching effect. The shell is then discretized via Lagrange equations of motion to achieve the responses of the arterial wall. Numerical results are given in two sections. First, the presented formulation is validated by conducting a comparative study on a single-layer compressible pressurized shell. Close agreement between the outcomes of the developed model with those provided by finite element (FE) simulation signifies the necessity of incorporating thickness deformation in the higher order shell theory. In the next step, by considering the artery as a two-layer cylindrical shell comprising the media (the middle layer of the artery) and the adventitia (the outer layer), mechanical responses of an arterial wall subjected to an internal pressure are appraised through a number of parametric studies.