bulging and bending of a thick-walled cylinder with residual stress under combined extension and inflation

Bifurcation is a localized instability that has been extensively studied. however, this sort of instability was not given sufficient consideration in the presence of residual stresses, particularly generalized non-planar residual stresses. this study aims to investigate the bifurcation phenomena in hyperelastic materials subjected to generalized residual stresses. residual stresses predominantly arise in arterial wall tissue due to various factors, including growth and development. these residual stresses influence the mechanical response of hyperelastic materials and play a crucial role in the locus of the bulge along a bifurcating cylindrical tube. in this paper, the impact of the mechanical behavior and residual stresses on bifurcation instability with application to aneurysms is investigated. the analysis employs numerical simulations grounded in a proposed methodology integrated into the finite element code through a user-defined material subroutine. the finite element modeling utilizes the commercial software abaqus and applies the modified riks method. the results show that bending is the initial bifurcation mode for relatively small axial stretches, while at higher stretches the (pure) bulging mode is more likely, serving as the lower bound. for small stretches, if bending is prevented, the bulging that occurs requires higher internal pressures than when bending is allowed, indicating that avoiding bending may delay aneurysm formation. post-bending bulges developing sideways in the studied cylinders resemble abdominal aortic aneurysms, whereas balloon-shaped bulges in (pure) bulging modes are associated with arterial rupture.