Polindara César, Waffenschmidt Tobias, Menzel Andreas
Institute of Mechanics, Department of Mechanical Engineering, TU Dortmund, Leonhard-Euler-Str. 5, D-44227 Dortmund, Germany.
Institute of Mechanics, Department of Mechanical Engineering, TU Dortmund, Leonhard-Euler-Str. 5, D-44227 Dortmund, Germany; 3M Deutschland GmbH, Carl-Schurz-Str. 1, D-41453 Neuss, Germany.
J Biomech. 2016 Aug 16;49(12):2341-8. doi: 10.1016/j.jbiomech.2016.01.037. Epub 2016 Feb 12.
In this contribution we study the balloon angioplasty in a residually stressed artery by means of a non-local gradient-enhanced fibre damage model. The balloon angioplasty is a common surgical intervention used to extend or reopen narrowed blood vessels in order to restore the continuous blood flow in, for instance, atherosclerotic arteries. Inelastic, i.e. predominantly damage-related and elastoplastic processes are induced in the artery during its inflation resulting in an irreversible deformation. As a beneficial consequence, provided that the inelastic deformations do not exceed a specific limit, higher deformations can be obtained within the same pressure level and a continuous blood flow can be guaranteed. In order to study the mechanical response of the artery in this scenario, we make use of the non-local gradient-enhanced model proposed in Waffenschmidt et al. (2014). In this contribution, we extend this model to make use of an incompressible format in connection with a Q1Q1P0 finite element implementation. The residual stresses in the artery are also taken into account following the framework presented in Waffenschmidt (2015). From the results it becomes apparent that, when the artery is subjected to radial stresses beyond the physiological range, damage evolution is triggered in the collagen fibres. The impact of the residual stresses on the structural response and on the circumferential stress distribution along the thickness of the arterial wall is also studied. It is observed that the residual stresses have a beneficial effect on the mechanical response of the arterial wall.
在本论文中，我们借助非局部梯度增强纤维损伤模型研究了残余应力动脉中的球囊血管成形术。球囊血管成形术是一种常见的外科手术干预手段，用于扩张或重新开通狭窄的血管，以恢复例如动脉粥样硬化动脉中的持续血流。在动脉膨胀过程中会引发非弹性（即主要与损伤相关的）以及弹塑性过程，从而导致不可逆变形。一个有益的结果是，只要非弹性变形不超过特定限度，在相同压力水平下就可以获得更大的变形，并且能够保证持续的血流。为了研究这种情况下动脉的力学响应，我们采用了瓦芬施密特等人（2014年）提出的非局部梯度增强模型。在本论文中，我们扩展了该模型，使其与Q1Q1P0有限元实现相结合，采用不可压缩格式。动脉中的残余应力也按照瓦芬施密特（2015年）提出的框架予以考虑。从结果可以明显看出，当动脉受到超出生理范围的径向应力时，胶原纤维中会引发损伤演化。我们还研究了残余应力对结构响应以及沿动脉壁厚度的周向应力分布的影响。观察到残余应力对动脉壁的力学响应具有有益作用。
