超弹性薄壁圆管局部起鼓形态的稳定性分析和实验研究

Hyperelastic membrane tube structures are widely used in modern engineering and everyday life. They also have promising applications in medical engineering and extra-terrestrial use. Localized bulging of an inflated hyperelastic membrane tube shares the same mathematical and mechanical features with a variety of other strain localization phenomena in engineering structures and materials. Recent work by the principal investigator has shown that on the one hand localized bulging of an inflated membrane tube is a nonlinear bifurcation phenomenon, and on the other hand, such localization is highly sensitive to various imperfections. The present project aims at further understanding how different loading and end conditions, and different material and geometrical imperfections affect the bifurcation pressure, and the stability properties of the localized bulging configurations. The results to be obtained will replace and further extend existing experimental results which are classical but out of date. They will help understand a variety of other strain localization phenomena associated with more complex geometries and constitutive relations. As one application, the new results will help understand the mechanisms that lead to the formation of aneurysms after pathological changes have locally weakened the arterial wall. As preparatory work before experiments are carried out on live arteries, the present research will help provide the necessary theoretical and experimental underpinnings for future development of drugs that can be used to inhibit aneurysm initiation, and further growth in the case when an aneurysm has already formed.

超弹性薄壁管是现代工程和日常生活中经常使用的结构，在航天及医疗领域更有广泛的应用前景。受内压时，薄壁圆管会发生局部起鼓，这种局部化现象又与许多其它工程结构和材料中的局部化现象具有相同的数学和力学特征。项目申请人近期的工作一方面证明了薄壁圆管起鼓其实是一个非线性分叉现象，又初步展示了这类失稳对各类缺陷的高度敏感性。本项目旨在通过数学分析和实验验证相结合的方法，进一步弄清超弹性薄壁圆管在各种加载和边界条件下，以及各种几何和材料缺陷情况下导致起鼓的临界载荷的变化规律，和起鼓形态的稳定性。研究结果将取代目前文献中已经过时的经典实验结果并加以推广，对了解一大类本构关系和几何形状更为复杂的局部化问题具有重要的指导意义。作为应用之一，最新结果将有助于了解主动脉因病变导致脉壁变薄变弱后局部起鼓的机理。作为用实体动脉进行实验前的前期工作，该项目的成果将对今后研发抑制动脉瘤发生和生长的药物具有指导意义。

超弹性软管在受内压时往往会发生局部起鼓。对它进行深入研究既可以帮助理解更为复杂的局部化现象（如相变），其研究本身也有许多用途，比如可以解释人体内急性动脉瘤的发生和破裂机理。以前所有有关超弹性软管局部起鼓的研究都没有认识到局部起鼓是一个分岔现象，因此现有的结果存在一些不足，甚至错误的地方。本项目旨在通过数学分析，实验验证和数值模拟相结合的方法，彻底弄清超弹性圆管在各种加载和边界条件下，以及各种几何和材料缺陷情况下导致起鼓的临界载荷的变化规律，和起鼓形态的稳定性，更新目前文献中已经过时的经典实验结果并进行推广。.该项目到目前为止已获得了以下主要成果：（1） 首次借助于动力系统理论推导出任意厚度软管起鼓的分叉条件，并用它阐明了薄膜理论的适用范围；（2）研究了纤维增强对起鼓的抑制作用，解释了健康动脉不会起鼓的设计原理；（3）验证了起鼓临界压力对缺陷的高度敏感性，扩展压力对缺陷的不敏感性，以及软管端部条件对起鼓的影响；（4）研究了管内流体流动对起鼓的稳定作用；（5）阐明了管壁局部缺陷对起鼓的影响，以及起鼓解的稳定性；（6）搭建的一整套实验平台，为今后的后续研究打下了良好的基础。