Abstract We establish the existence of an internal uniform hydrostatic state of stress inside a coated non-parabolic open elastic inhomogeneity when the surrounding matrix is subjected to a concentrated couple and uniform remote in-plane stresses. The proof of existence is accomplished through analytic continuation and the introduction of a specialized form of the conformal mapping function containing an infinite number of first-order poles. The complex constants appearing in the mapping function can be uniquely determined from a resulting set of non-linear recurrence relations for given material, geometric and loading parameters. The convergence criterion for the series in the mapping function is rigorously established. A simple condition on the remote loading in the matrix is found for given elastic constants of the inhomogeneity and the matrix in order to ensure that the internal stresses inside the non-parabolic inhomogeneity are uniform and hydrostatic. The analysis indicates that the internal uniform hydrostatic stress field, the constant mean stress in the coating and the constant hoop stress along the inhomogeneity-coating interface on the coating side are all independent of the specific open shapes of the two interfaces and are also independent of the existence of the nearby concentrated couple. However, the non-parabolic open shapes of the two interfaces are significantly influenced by the concentrated couple. We also accomplish the design of an uncoated non-parabolic harmonic elastic inhomogeneity in the presence of an arbitrary number of concentrated couples applied in the matrix.

中文翻译：

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集中耦合附近涂层非抛物线不均匀性内的均匀静水应力

摘要 我们建立了当周围基体受到集中耦合和均匀远程面内应力时，涂层非抛物线开放弹性不均匀性内部存在内部均匀流体静力学应力状态。存在证明是通过解析延拓和引入包含无限数量一阶极点的保形映射函数的特殊形式来完成的。对于给定的材料、几何和载荷参数，映射函数中出现的复杂常数可以从一组非线性递推关系的结果中唯一确定。严格建立映射函数中级数的收敛准则。对于给定的非均匀性和矩阵的弹性常数，找到了矩阵中远程加载的一个简单条件，以确保非抛物线非均匀性内部的内应力是均匀的和流体静力的。分析表明，涂层内均匀静水应力场、涂层中的恒定平均应力和沿涂层侧不均匀涂层界面的恒定环向应力均与两个界面的具体开放形状无关，也与附近集中夫妻的存在。然而，两个界面的非抛物线开放形状受到集中耦合的显着影响。