A circular inclusion with inhomogeneous non-slip imperfect interface in harmonic materials

作者：McArthur D R; Sudak L J^*

来源：Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 2016, 472(2190): 20160285.

DOI：10.1098/rspa.2016.0285

• inclusion
• imperfect interface
• harmonic materials
• complex variables

In this work, a rigorous study is presented for the problem associated with a circular inclusion embedded in an infinite matrix in finite plane elastostatics where both the inclusion and matrix are comprised a harmonic material. The inclusion/matrix boundary is treated as a circumferentially inhomogeneous imperfect interface that is described by a linear spring-type imperfect interface model where in the tangential direction, the interface parameter is infinite in magnitude and in the normal direction, the interface parameter is finite in magnitude (the so-called non-slip interface condition). Through the repeated use of the technique of analytic continuation, the boundary value problem for four analytic functions is reduced to solve a single first-order linear ordinary differential equation with variable coefficients for a single analytic function defined within the inclusion. The unknown coefficients of said function are then found via various analyticity requirements. The method is illustrated, using a specific example of a particular class of inhomogeneous non-slip imperfect interface. The results from these calculations are then contrasted with the results from the homogeneous imperfect interface. These comparisons indicate that the circumferential variation of interface damage has a pronounced effect on the average boundary stress.

• 出版日期2016-6-1