Modelling of residually stressed, extended and inflated cylinders with application to aneurysms

Abstract

The paper presents the localized bifurcation abnormal enlargement associated with certain human diseases such as abdominal aortic aneurysms (AAA), among others. The constitutive framework herewith proposed is constructed relying on the modelling of non-linear elastic materials under the action of residual stresses. The suitable incorporation on the mechanical response of residual stresses in the analysis is regarded important for the formation of aneurysms in soft tissues. From a mechanical perspective, the onset of aneurysms formation can be interpreted through bifurcation conditions, whose localization is relatively sensitive to different material and geometrical parameters as it is shown here. In order to reduce the risk and interpret aneurysm formation, we perform a thorough sensitivity analysis of the effect of design parameters such as tube diameter, length, thickness and strength of the residual stress field on bifurcation of a tube under inflation and extesion. A consistent residually stressed material model is formulated in terms of invariants for a general elastic strain-energy function. The dependence of applied pressure, axial stretch and different geometrical and constitutive parameters on bulging and bending bifurcation is illustrated. The numerical procedure to analyse the bifurcation of the finite deformation boundary-value problem at hand is developed based on the modified Riks method. The proposed formulation is implemented in the general-purpose finite element code ABAQUS using user-defined material subroutines.For a given material model, bulging bifurcation is expected for sufficiently large values of the axial stretch while the onset of bifurcation is found to be the bending mode for small values of the axial stretch. This transition zone from bending bifurcation to bulging bifurcation is analyzed for the different parameters considered.