论文标题
相邻圆柱体之间的Stokes流动的应力浓度的定量估计值
Quantitative estimates for stress concentration of the Stokes flow between adjacent circular cylinders
论文作者
论文摘要
当两个具有高对比度材料特性的夹杂物彼此靠近均匀介质时，在它们之间的狭窄区域中，应力可能会变得很大。在本文中，当夹杂物是相同半径的圆缸的二维横截面时，我们研究了二维Stokes流动中的这种应力浓度，而背景速度场是线性的。我们构建了两个矢量值函数，这些函数完全捕获了应力的奇异行为，并在这些功能方面为应力提供了渐近表示公式，因为两个圆柱体之间的距离趋于零。然后，我们使用表示公式表明，应力总是通过证明应力张量的压力或剪切应力成分吹来的。爆炸率显示为$δ^{ - 1/2} $，其中$δ$是两个气缸之间的距离。据我们所知，这项工作是第一个严格地在狭窄区域中逐渐得出渐近解决方案的Stokes流动。
When two inclusions with high contrast material properties are located close to each other in a homogeneous medium, stress may become arbitrarily large in the narrow region between them. In this paper, we investigate such stress concentration in the two-dimensional Stokes flow when inclusions are the two-dimensional cross sections of circular cylinders of the same radii and the background velocity field is linear. We construct two vector-valued functions which completely capture the singular behavior of the stress and derive an asymptotic representation formula for the stress in terms of these functions as the distance between the two cylinders tends to zero. We then show, using the representation formula, that the stress always blows up by proving that either the pressure or the shear stress component of the stress tensor blows up. The blow-up rate is shown to be $δ^{-1/2}$, where $δ$ is the distance between the two cylinders. To our best knowledge, this work is the first to rigorously derive the asymptotic solution in the narrow region for the Stokes flow.
