Computational modeling of a residually stressed thick-walled cylinder under the combined action of axial extension and inflation

Abstract

Previous studies have shown that the mechanical response of incompressible hyperelastic materials is affected by the occurrence of residual stresses. In the context of biological soft tissues, such residual stresses result from factors that include growth and development processes. The detailed effect of these initial stresses on mechanical behavior remains to be explored in detail. The magnitude and distribution of residual stresses in arterial wall tissue affect the location of the occurrence of instabilities such as bulges. This study aims to develop a new approach to assess material behavior during bifurcation instability in the presence of residual stresses, especially non-planar stresses. A finite element protocol is developed for bifurcation and post-bifurcation of residually stressed thick-walled hyper-elastic circular hollow tubes subjected to axial stretches and internal pressure, incorporating three-dimensional residual stresses. A constitutive equation based on the strain energy function for these tubes is formulated and implemented in ABAQUS, using the Modified Riks method and a user-defined material subroutine (UMAT). Results indicate that bending bifurcation is likely for small axial stretches but becomes less probable with larger axial stretches while bulging bifurcation is expected for all axial stretch values. Pressures associated with pure bulging modes are higher than those for bulging induced by bending, suggesting aneurysms can be delayed by avoiding bending bifurcation. The bulging from bending bifurcation occurs on one side of the tubes, reflecting abdominal aortic aneurysm (AAA) conditions. The unsymmetrical bulge development aligns with the methodology used, whereas balloon-like bulging in pure modes is linked to arterial rupture.