二维刚性夹杂间应力集中的渐近分析
Asymptotic analysis of the stress concentration between two adjacent stiff inclusions in all dimensions
摘要：
在两个紧密定位的刚性夹杂物之间的区域中，当夹杂物界面边界之间的距离趋于零时，应力（部分无限系数的Lamé系统解的梯度）可能变得任意大。本文的主要目的是给出一个清晰的描述的应力集中的渐近行为，当界面之间的夹杂物边界的距离趋于零。为此，我们捕获所有的爆破因子矩阵，其元素包括某些积分的情况下，当两个包含接触的解决方案。然后，我们能够建立的渐近公式的应力集中存在两个紧接触的$m$凸夹杂在所有的维度。此外，还给出了一个四舍五入的曲线正方形的例子，以供将来在数值计算和模拟中应用。
英文摘要：
In the region between two closely located stiff inclusions, the stress, which is the gradient of a solution to the Lamé system with partially infinite coefficients, may become arbitrarily large as the distance between interfacial boundaries of inclusions tends to zero. The primary aim of this paper is to give a sharp description in terms of the asymptotic behavior of the stress concentration, as the distance between interfacial boundaries of inclusions goes to zero. For that purpose we capture all the blow-up factor matrices, whose elements comprise of some certain integrals of the solutions to the case when two inclusions are touching. Then we are able to establish the asymptotic formulas of the stress concentration in the presence of two close-to-touching $m$-convex inclusions in all dimensions. Furthermore, an example of curvilinear squares with rounded-off angles is also presented for future application in numerical computations and simulations.
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