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**Stress field of a coated arbitrary shape inclusion.**
*(English)*
Zbl 1271.74045

Summary: This paper presents an effective method for the plane problem of a coated inclusion of arbitrary shape embedded in an isotropic matrix subjected to uniform stresses at infinity. Based on the complex variable method combined with the expansion of Faber series and Laurent series, the complex potentials in the matrix, the coating and the arbitrary shape inclusion are given in the form of series with unknown coefficients. The stress and displacement continuous conditions on the interfaces are then used to produce a set of linear equations containing all the coefficients. Through solving these linear equations, the complex potentials are finally obtained in the three phases. Additionally, numerical results are presented and graphically shown to investigate the influence of inclusion geometry and coating on the stress distribution along the interfaces for the cases of a coated elliptic, square and triangle inclusions, respectively. It is found that the coating has little effects on the interface stress for a hard inclusion, while it impacts greatly for a soft inclusion. Especially, it is also found that the stresses show the nature of intense fluctuations near the corner of the triangle inclusion, since the inclusion in this case is similar to a wedge.

### MSC:

74E05 | Inhomogeneity in solid mechanics |

74S70 | Complex-variable methods applied to problems in solid mechanics |

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\textit{J.-C. Luo} and \textit{C.-F. Gao}, Meccanica 46, No. 5, 1055--1071 (2011; Zbl 1271.74045)

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