The goal of this contribution is to propose a method for the numerical simulation of residual stresses in arterial walls. Generally, when axial segments of arterial walls are sliced in radial direction they spring open, which has been observed firstly in Vaishnav & Vossoughi [
]. Thus, residual stresses have to exist in the unloaded configuration. As often stated in the literature an open artery governed by a radial cut can be assumed to be stress-free. In this contribution we firstly close the gap between the opened transmural surfaces of a sliced artery by a displacement-driven procedure introducing some kind of interface elements formulated in the relative displacement of associated nodal points. Then we construct a new mesh of the closed artery and apply a method to incorporate the residual stresses without using the interface elements. This is advantageous for further numerical simulations as e.g., applying an internal pressure.
Due to the special composition, orientation and weak interaction of particular fibers within arterial walls we consider the superposition of two transversely isotropic hyperelastic stored energy functions for the description of the anisotropic hyperelastic behavior in the physiological range of deformations. In order to guarantee the existence of solutions of underlying boundary value problems we use the functions proposed in Balzani, Neff, Schröder & Holzapfel [
], which fit into the concept of polyconvexity. When arteries are overstretched, e.g., during a balloon-angioplasty, then deformations occur which are not in the physiological range anymore, and a discontinuous damage effect is observed. Therefore, the thermodynamically consistent anisotropic damage model introduced in Balzani, Schröder & Gross [
] is applied to the polyconvex stored energy. The basic assumption of the damage model is that the damage occurs mainly in fiber direction. As a numerical example we consider the cross-section of a diseased artery in order to give an impression of the performance of the model.