In this investigation, the mechanical modelling of a hyperelastic residually stressed thick-walled circular cylindrical tube under inflation and extension is performed from a numerical standpoint. The constitutive relation is derived for residually stressed solids using an invariant-based free energy approach. A three-dimensional residual stress field is introduced in the argument of the free-energy function. This formulation is incorporated into a numerical procedure using the Finite Element Method (FEM), with the use of a nonlinear solution scheme via the modified Riks method in order to capture bifurcation and post-bifurcation of the tube. The FE implementation of the proposed formulation is carried out in the general purpose code ABAQUS by means of user-defined capabilities. A comprehensive analysis of the structural performance of the tube is conducted with special focus on the effect of the residual stresses on the bifurcation behaviour. Results are analysed mainly in the context of aneurysms formation and propagation in arterial wall tissues, although it has other applications such as in the context of venous tortuosity. Bulging and bending modes are obtained, and post-bifurcation is also captured. Results suggest that the onset and location of the bulge along the axis of the tube depend mainly on the axial stretch and on the residual stress field. Computations also show that for sufficiently large values of axial stretch the onset of bifurcation is bulging while for small values of axial stretch the onset of bifurcation is bending. Post-bifurcation behaviour of this latter case gives rise to bulges on one side of the tube, which is an irregular shape that appears in the advancement of abdominal aortic aneurysms (AAA).

在这项研究中，从数值角度对膨胀和伸展下的超弹性残余应力厚壁圆柱管进行机械建模。使用基于不变量的自由能方法为残余应力固体推导出本构关系。在自由能函数的自变量中引入了三维残余应力场。该公式结合到使用有限元方法 (FEM) 的数值程序中，并通过改进的 Riks 方法使用非线性求解方案，以捕获管的分叉和后分叉。拟议公式的 FE 实现在通用代码ABAQUS 中进行通过用户定义的功能。对管的结构性能进行了综合分析，特别关注残余应力对分叉行为的影响。结果主要在动脉壁组织中动脉瘤形成和传播的背景下进行分析，尽管它还有其他应用，例如在静脉曲折的背景下。获得了膨胀和弯曲模式，并且还捕获了后分叉。结果表明，沿管轴的凸起的开始和位置主要取决于轴向拉伸和残余应力场。计算还表明，对于足够大的轴向拉伸值，分叉的起点是凸出的，而对于较小的轴向拉伸值，分叉的起点是弯曲​​的。