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.

中文翻译：

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应用于动脉瘤的残余应力、扩展和膨胀圆柱体的建模

摘要 本文介绍了与某些人类疾病相关的局部分叉异常增大，例如腹主动脉瘤 (AAA) 等。在此提出的本构框架是依赖于在残余应力作用下非线性弹性材料的建模而构建的。在分析中适当结合残余应力的机械响应被认为对于软组织中动脉瘤的形成很重要。从力学的角度来看，动脉瘤形成的开始可以通过分叉条件来解释，其定位对不同的材料和几何参数相对敏感，如这里所示。为了降低风险和解释动脉瘤的形成，我们对管径、长度、厚度和残余应力场强度等设计参数对膨胀和拉伸下管子分叉的影响进行了彻底的敏感性分析。一致的残余应力材料模型是根据一般弹性应变-能量函数的不变量来制定的。说明了施加的压力、轴向拉伸和不同的几何和本构参数对膨胀和弯曲分叉的依赖性。基于改进的 Riks 方法开发了用于分析手头有限变形边界值问题的分岔的数值程序。建议的公式是在通用有限元代码 ABAQUS 中使用用户定义的材料子程序实现的。 对于给定的材料模型，对于足够大的轴向拉伸值，预计会出现膨胀分叉，而发现分叉的开始是轴向拉伸值较小的弯曲模式。针对所考虑的不同参数分析了从弯曲分叉到凸出分叉的这个过渡区。