Stress field of a coated arbitrary shape inclusion.

*(English)*Zbl 1271.74045Summary: 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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##### References:

[1] | Chao, CK; Chen, FM; Shen, MH, Circularly cylindrical layered media in plane elasticity, Int J Solids Struct, 43, 4739-4756, (2006) · Zbl 1120.74414 |

[2] | Jiang, CP; Cheung, YK, An exact solution for the three-phase piezoelectric cylinder model under antiplane shear and its applications to piezoelectric composites, Int J Solids Struct, 38, 4777-4796, (2001) · Zbl 1020.74016 |

[3] | Ru, CQ, Three-phase elliptical inclusions with internal uniform hydrostatic streses, J Mech Phys Solids, 47, 259-273, (1999) · Zbl 0964.74022 |

[4] | Jiang, CP; Tong, ZH; Cheung, YK, A generalize self-consistent method for piezoelectric fiber reinforced composites under antiplane shear, Mech Mater, 33, 295-308, (2001) |

[5] | Sudak, LJ, Effect of an interphase layer on the electroelastic stresses within a three-phase elliptic inclusion, Int J Eng Sci, 41, 1019-1039, (2003) |

[6] | Chen, TY, A confocally multicoated elliptical inclusion under antiplane shear: some new results, J Elast, 74, 87-97, (2004) · Zbl 1058.74523 |

[7] | Shen, MH; Chen, SN; Chen, FM, Piezoelectric study on confocally multicoated elliptical inclusion, Int J Eng Sci, 43, 1299-1312, (2005) |

[8] | Yang, BH; Gao, CF, Anti-plane electro-elastic field in an infinite matrix with N coated-piezoelectric inclusions, Compos Sci Technol, 69, 2668-2674, (2009) |

[9] | Chao, CK; Chen, FM; Shen, MH, An exact solution for thermal stresses in a three-phase composite cylinder under uniform heat flow, Int J Solids Struct, 44, 926-940, (2007) · Zbl 1124.74013 |

[10] | Ru, CQ, Effect of interphase layers on thermal stresses within an elliptical inclusion, J Appl Phys, 84, 4872-4879, (1998) |

[11] | Shen, H; Schiavone, P; Ru, CQ; Mioduchowski, A, Interfacial thermal stress analysis of an elliptic inclusion with a compliant interphase layer in plane elasticity, Int J Solids Struct, 38, 7587-7606, (2001) · Zbl 1011.74015 |

[12] | Xiao, ZM; Bai, J, Numerical simulation on a coated piezoelectric sensor interacting with a crack, Finite Elem Anal Des, 38, 691-706, (2002) · Zbl 1100.74647 |

[13] | Liu, YW; Song, HP; Fang, QH; Jin, B, Shielding effect and emission condition of a screw dislocation near a blunt crack in elliptical inhomogeneity, Meccanica, 45, 519-530, (2010) · Zbl 1258.74190 |

[14] | Qin, QH; Wang, JS; Li, XL, Effect of elastic coating on fracture behavior of piezoelectric fiber with a penny-shaped crack, Compos Struct, 75, 465-471, (2006) |

[15] | Villaggio, P, The rigid inclusion with highest penetration, Meccanica, 26, 149-153, (1991) |

[16] | Ru, CQ, Eshelby inclusion of arbitrary shape in an anisotropic plane or half-plane, Acta Mech, 160, 219-234, (2003) · Zbl 1064.74039 |

[17] | Pan, E, Eshelby problem of polygonal inclusions in anisotropic piezoelectric full and half-planes, J Mech Phys Solids, 52, 567-589, (2004) · Zbl 1074.74017 |

[18] | Gao, CF; Noda, N, Faber series method for two-dimensional problems of an arbitrarily shaped inclusion in piezoelectric materials, Acta Mech, 171, 1-13, (2004) · Zbl 1085.74014 |

[19] | Luo, JC; Gao, CF, Faber series method for plane problems of an arbitrarily shaped inclusion, Acta Mech, 208, 133-145, (2009) · Zbl 1397.74040 |

[20] | Shen, MH; Chen, FM; Hung, SY, Piezoelectric study for a three-phase composite containing arbitrary inclusion, Int J Mech Sci, 52, 561-571, (2010) |

[21] | Muskhelishvili NI (1975) Some basic problems of the mathematical theory of elasticity. Groningen, Noordhoff · Zbl 0297.73008 |

[22] | Curtiss, JH, Faber polynomials and the Faber series, Am Math Mon, 78, 577-596, (1971) · Zbl 0215.41501 |

[23] | Kosmodamianskii AS, Salorov SA (1983) Thermal stress in connected multiply plates. Vishcha Shkola, Kiev (in Russian) |

[24] | Savin GN (1961) Stress concentration around holes. Pergamon Press, London · Zbl 0124.18303 |

[25] | Chen, DH; Nisitani, H, Singular stress field near the corner of jointed dissimilar materials, ASME J Appl Mech, 60, 609-613, (1993) · Zbl 0795.73057 |

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