Abstract
This paper presents the theoretical and numerical results for the plane problem of an arbitrarily shaped inclusion in an infinite isotropic matrix based on the Faber series method. The key of the method is to express the complex potentials in the arbitrary inclusion in the form of Faber series with unknown coefficients and then substitute them directly into the boundary conditions on the interface. These conditions lead to a set of linear equations containing all the unknown coefficients. Through solving these linear equations, one can obtain the complex potentials both inside the inclusion and in the matrix. Then, numerical results are presented and graphically shown for the cases of an elliptic, square, and triangle inclusions, respectively. It is found that as the stiffness of the inclusion increases, the hoop stress decreases at the rim of the inclusion, while the radial and shear stresses increase. Especially, it is also found that the stresses show the nature of intense fluctuations near the corners of the triangle inclusion, since the inclusion in this case is similar to a wedge.
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A commentary to this article can be found online at http://dx.doi.org/10.1007/s00707-012-0663-7.
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Luo, J.C., Gao, C.F. Faber series method for plane problems of an arbitrarily shaped inclusion. Acta Mech 208, 133–145 (2009). https://doi.org/10.1007/s00707-008-0138-z
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DOI: https://doi.org/10.1007/s00707-008-0138-z