Wang Xu, Schiavone Peter
School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai, China.
Department of Mechanical Engineering, University of Alberta, Edmonton, AB, Canada.
Math Mech Solids. 2023 Nov;28(11):2396-2403. doi: 10.1177/10812865231166081. Epub 2023 Apr 26.
We propose an effective method for the solution of the plane problem of an edge dislocation in the vicinity of a circular inhomogeneity with Steigmann-Ogden interface. Using analytic continuation, the pair of analytic functions defined in the infinite matrix surrounding the inhomogeneity can be expressed in terms of the pair of analytic functions defined inside the circular inhomogeneity. Once the two analytic functions defined in the circular inhomogeneity are expanded in Taylor series with unknown complex coefficients, the Steigmann-Ogden interface condition can be written explicitly in complex form. Consequently, all of the complex coefficients appearing in the Taylor series can be uniquely determined so that the two pairs of analytic functions are then completely determined. An explicit and general expression of the image force acting on the edge dislocation is derived using the Peach-Koehler formula.
我们提出了一种有效的方法来解决具有Steigmann - Ogden界面的圆形不均匀性附近的边缘位错平面问题。通过解析延拓，在不均匀性周围的无限矩阵中定义的一对解析函数可以用在圆形不均匀性内部定义的一对解析函数来表示。一旦在圆形不均匀性中定义的两个解析函数用未知复系数展开为泰勒级数，Steigmann - Ogden界面条件就可以以复形式明确写出。因此，泰勒级数中出现的所有复系数都可以唯一确定，从而两对解析函数就完全确定了。利用皮奇 - 科勒公式推导出作用在边缘位错上的像力的显式通用表达式。
