Abstract
Using Stroh's formalism the simple explicit expressions of Green's functions for a 2D piezoelectric body with two semi-infinite fixed conductor cracks subjected to a generalized line force were given. The Coulomb force acting on the free line charge aroused by the piezoelectricity and the distributed boundary polarization charges was discussed at first. Interactions between two singularities with free charge (s) located in a region with external cracks were studied, too. The numerical results show that the Coulomb force for two or more singularities with one free charge at least will have much influence on the electrochemical fields in piezoelectric media when these singularities move closely with each other and therefore cannot be overlooked again. The solutions obtained are valid not only for plane and anti-plane problems but also for coupled problems between in-plane and out-of-plane deformations.
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References
Barnett D M, Lothe J. Dislocations and line charges in anisotropic piezoelectric insulators[J].Phys Status Solidi, Ser B, 1975,67(1): 105–111.
Chadwick P, Smith G D. Foundations of the theory of surface waves in anisotropic medium [J].Adv Appl Mech, 1977,17:303–377.
Hu Yuantai, Huang Yuying, Chen Chuanyao,et al. Green's functions for a piezoelectric semi-infinite body with a fixed conductor surface[J].Mechanics Research Communications, 2000,27(3): 333–338.
Hu Yuantai, Zhao Xinghua. Green's functions of two-dimensional anisotropic body with a parabolic boundary [J].Applied Mathematics and Mechanics (English Edition), 1996,17 (5):393–402.
Hwu C, Yen WJ. Green's functions of two-dimensional anisotropic plates containing an elliptic hole[J].International Journal of Solids and Structures, 1991,27 (13): 1785–1791.
Ting T C T. Image singularities of Green's functions for anisotropic elastic half-spaces and bimaterials[J].Journal of Elasticity, 1991,27(2): 119–139.
Ting T C T, Hu Yuantai, Kirchner H O K. Anisotropic elastic materials with a parabolic or hyperbolic boundary: a classical problem revisited[J].J Appl Mech, 2001,68(4): 537–542.
Chung M Y, Ting T C T. Piezoelectric solid with an elliptic inclusion or hole[J].International Journal of Solids and Structures, 1996,33(23):3343–3361.
Kuo C M, Barnett D M. Stress singularities of interfacial cracks in bonded piezoelectric half-spaces[A]. In: Wu J J, Ting T C T, Barnett D M (eds).Modern Theory of Anisotropic Elasticity and Applications, Philadelphia: SIAM, 1990, 33–50.
Park Y E. Linear electro-elastic fracture mechanics of piezoelectric materials[J].International Journal of Fracture, 1992,54: 79–100.
Park S B, Sun C T. Effect of electric field on fracture of piezoelectric ceramics[J].International Journal of Fracture, 1995,70(3): 203–216.
Sosa H, Khutoryansky N. New developments concerning piezoelectric materials with defects [J].International Journal of Solids and Structures, 1996,33:3399–3414.
Suo Z, Kuo C M, Barnett D M,et al. Fracture Mechanics for piezoelectric ceramics[J].Journal of Mechanics and Physics of Solids, 1992,40(4): 739–765.
Stroh A N. Dislocations and cracks in anisotropic elasticity[J].Phil Mag, 1958,3(30): 625–646.
Stroh A N. Steady state problem in anisotropic elasticity[J].J Math Phys, 1962,41(1): 77–103.
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Communicated by GUO Xing-ming
Project supported by the National Natural Science Foundation of China (No. 10172036) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry
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Yuan-tai, H., Guo-qing, L., Shu-nong, J. et al. Interaction of electric charges in a piezoelectric with rigid external cracks. Appl Math Mech 26, 996–1006 (2005). https://doi.org/10.1007/BF02466412
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DOI: https://doi.org/10.1007/BF02466412