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Solutions to a limited-permeable crack or two limited-permeable collinear cracks in piezoelectric/piezomagnetic materials

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Abstract

The solutions of a limited-permeable crack (case I) or two collinear limited-permeable cracks (case II) in piezoelectric/piezomagnetic materials subjected to a uniform tension loading were investigated in this paper using the generalized Almansi’s theorem. At the same time, the electric permittivity and the magnetic permeability of air in crack were firstly considered. Through the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations, in which the unknown variables were jumps of displacements across crack surfaces, not the dislocation density functions or the complex variable functions. To solve the dual integral equations, the jumps of displacements across crack surfaces were directly expanded in a series of Jacobi polynomials to obtain the relations among electric displacement intensity factors, magnetic flux intensity factors and stress intensity factors at crack tips.

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Authors and Affiliations

  1. Center for Composite Materials and Structures, Harbin Institute of Technology, P. O. Box 3010, 150080, Harbin, People’s Republic of China

    Zhen-Gong Zhou, Pei-Wei Zhang & Lin-Zhi Wu

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  1. Zhen-Gong Zhou
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  2. Pei-Wei Zhang
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  3. Lin-Zhi Wu
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Correspondence to Zhen-Gong Zhou.

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Zhou, ZG., Zhang, PW. & Wu, LZ. Solutions to a limited-permeable crack or two limited-permeable collinear cracks in piezoelectric/piezomagnetic materials. Arch Appl Mech 77, 861–882 (2007). https://doi.org/10.1007/s00419-007-0135-z

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  • DOI: https://doi.org/10.1007/s00419-007-0135-z

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