Analytical solution for a rigid line inclusion embedded in an infinite-extended plane under non-uniform loading is still a challenging problem in inclusion mechanics, which has both theoretical and applied significance in material engineering. In this paper, by directly employing Kolosov–Muskhelishvili stress potentials, a rigid line inclusion interacting with a generalized singularity is addressed in the framework of plane deformation, with the help of the superposition principle. It should be pointed out that the generalized singularity in this study can represent a point force, an edge dislocation, a point moment, a point nucleus of strain, and even remote uniform load, etc. The solutions can be used as kernel functions for integral equation formulations of rigid line inclusion–substrate system models using the Green’s function method. With this framework, stress field and stress intensity factors at the line inclusion ends are analyzed. The application of the solutions is demonstrated with two simple examples: (i) the rigid line inclusion under remote loading is studied, and it is strictly confirmed with rigorous proof that the remote shear load will not arouse stress concentration; (ii) a rigid line inclusion interacting with a dislocation is investigated, and the full solution is given. These examples also partially validate the general solution derived this study.
Rigid line inclusion Generalized singularity Green’s function method Plane deformation
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This work is partially supported by National Natural Science Foundation of China (Grant No. 41630634).
Hasebe, N., Keer, L.M., Nemat-Nasser, S.: Stress analysis of a kinked crack initiating from a rigid line inclusion. Part I: formulation. Mech. Mater. 3, 131–45 (1984a)CrossRefGoogle Scholar
Hasebe, N., Nemat-Nasser, S., Keer, L.M.: Stress analysis of a kinked crack initiating from a rigid line inclusion. Part II: direction of propagation. Mech. Mater. 3, 147–56 (1984b)CrossRefGoogle Scholar
Hu, K.X., Chanra, A.: Interactions among general systems of cracks and anticrack: an integral equation approach. J. Appl. Mech. ASME 60, 920–929 (1993)CrossRefGoogle Scholar
Itou, H., Khludnev, A.M., Rudoy, E.M., Tani, A.: Asymptotic behaviour at a tip of a rigid line inclusion in linearized elasticity. Z. Angew. Math. Mech. 92, 716–730 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
Muskhelishvili, N.I.: Some Problems of Mathematical Theory of Elasticity (English Transl. from the third Russian edition). Noordhoff Ltd., Groningen (1953)Google Scholar
Nan, H.S., Wang, B.L.: Effect of interface stress on the fracture behavior of a nanoscale linear inclusion along the interface of biomaterials. Int. J. Solids Struct. 51, 4094–4100 (2014)CrossRefGoogle Scholar
Nishimura, N., Liu, Y.J.: Thermal analysis of carbon-nanotube composites using a rigid-line inclusion model by the boundary integral equation method. Comput. Mech. 35, 1–10 (2004)CrossRefzbMATHGoogle Scholar
Shodja, H.M., Ojaghnezhad, F.: A general unified treatment of lamellar inhomogeneities. Eng. Fract. Mech. 74, 1499–1510 (2007)CrossRefGoogle Scholar
Wang, Z.Y., Zhang, H.T., Chou, Y.T.: Characteristics of the elastic field of a rigid line inhomogeneity. J. Appl. Mech. ASME 52, 818–822 (1985)CrossRefGoogle Scholar
Zeng, J., Saltysiak, B., Johnson, W.S., Schiraldi, A., Kumar, S.: Processing and properties of poly(methyl methacrylate)/carbon nanofiber composites. Compos. B 35, 245–9 (2004)CrossRefGoogle Scholar