Material Volume Changes in Residually Stressed Idealized Arteries

Resumen

In this article, inflated, extended and residually stressed tubular structures are studied. Residual stresses are implemented with the help of the opening angle method. Firstly (in the first part of the paper), the residually stressed tube is considered to consist of a single layer, while the material is taken to be either isotropic or fiber-reinforced, and to undergo material volume changes applicable to swelling effects; this part aims to provide a basic understanding of the interplay between residual stresses and material volume changes. Secondly, the tube is taken to consist of two concentric fiber-reinforced layers, which applies to the modeling of arterial soft tissue. When dealing with fiber-reinforced materials, the stress-free (natural) configuration of the fibers may differ from that of the fiber-embedding ground substance. This is an additional mechanism that affects the residual stress field. The stiffness of the ground substance is taken to either stiffen, weaken, or remain unaffected by the material volume changes. All this allows us to study the relationship between residual stress distribution, material volume changes, and external loading (axial stretch and inflation pressure) on the structural response.