Methods to compute 3D residual stress distributions in hyperelastic tubes with application to arterial walls

In this paper the problem of modeling three-dimensional residual stress distributions in hyperelastic tubes is addressed. First, the problem of a radially opened straight and bent tube, where the opening angle depends on the axial position, is explored with the semi-inverse method. As a result a rather complicated system of nonlinear partial differential equations is achieved which is difficult to solve. Second, a different approximate method considers the tube as a composition of two, three, four or more rings in the axial direction. Also here the opening angle of the tube depends on the axial position. Some numerical solutions for the stress components in the radial, circumferential and axial directions are analyzed in more detail. Third, the tube wall is divided into a number of radial layers, with different mechanical properties, and an approximate method to treat that problems is presented. It is emphasized that the proposed approach can also be used to compute 3D residual stress distributions in arterial walls. A final conclusion points to possible future research directions.