Bifurcation and post-bifurcation of an inflated and extended residually-stressed circular cylindrical tube with application to aneurysms initiation and propagation in arterial wall tissue
Bifurcation and post-bifurcation of an inflated and extended residually-stressed circular cylindrical tube with application to aneurysms initiation and propagation in arterial wall tissue
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DOI：
10.1016/j.finel.2019.04.004
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发表时间：
2019-09-01
影响因子：
3.1
通讯作者：
Merodio, J.
中科院分区：
文献类型：
--
作者：
Dehghani, H.;Desena-Galarza, D.;Merodio, J.
研究了一种分析残余应力弹性体有限变形边值问题分叉和后分叉的数值方法。特别地，问题是经受径向和周向残余应力的圆柱形管的组合的延伸和膨胀。材料模型，由残余应力相关的非线性弹性本构关系的不变量，在有限元代码中实现。基于修正的Riks方法，发展了一种分析有限变形边值问题分支和后分支的数值方法。的分叉和分叉后的行为下的负载在手头上的残余应力管的依赖性示出，并与结果相比，当没有残余应力。有限变形边值问题主要描述在膨胀压力方面，以及管的轴向和方位向伸展。对于所涉及的参数（以无量纲形式）的不同值，特别是残余应力的强度，以图形方式说明了这些量对分叉的依赖性。据发现，胀形分叉预计足够大的值的轴向拉伸。另一方面，对于小的轴向拉伸值（接近非扩展配置），分叉的发病被发现是弯曲模式。此外，对于后一种情况下，在随后的运动，即分叉后，它示出，弯曲触发鼓，而不是弯曲的情况下，不允许和分叉的发病与鼓。此外，在弯曲分叉开始后分叉期间形成的隆起或异常增大出现在管的一侧，显示不规则形状，这与腹主动脉瘤（AAA）的发展一致。
A numerical procedure to analyze bifurcation and post-bifurcation of a finite deformation boundary-value problem for a residually-stressed elastic body is studied. In particular, the problem is the combined extension and inflation of a circular cylindrical tube subject to radial and circumferential residual stresses. The material model, given by a residual-stress dependent nonlinear elastic constitutive law in terms of invariants, is implemented in a finite element code. A numerical procedure to analyze the bifurcation and post-bifurcation of the finite deformation boundary-value problem at hand is developed based on the modified Riks method. The dependence of bifurcation and post-bifurcation behavior of tubes under the loading at hand on residual stresses is shown and compared with results when there is no residual stress. The finite deformation boundary-value problem is described mainly in terms of the inflation pressure, as well as the axial and azimuthal stretches of the tube. The dependence of these quantities on bifurcation is illustrated graphically for different values of the parameters (in dimensionless form) involved, in particular, the strength of the residual stress. It is found that bulging bifurcation is expected for sufficiently large values of the axial stretch. On the other hand, for small values of the axial stretch (close to the non-extended configuration), the onset of bifurcation is found to be the bending mode. Furthermore, for the latter case in subsequent motion, i.e. post-bifurcation, it is shown that bending triggers bulging as opposed to the situation in which bending is not allowed and the onset of bifurcation is associated with bulging. In addition, the bulge, or the abnormal enlargement, that is formed during post-bifurcation after the onset of bending bifurcation appears on one side of the tube showing an irregular shape which is consistent with the development of abdominal aortic aneurysms (AAA).