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Basic solutions of multiple parallel symmetric mode-III cracks in functionally graded piezoelectric/piezomagnetic material plane

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Abstract

The Schmidt method is adopted to investigate the fracture problem of multiple parallel symmetric and permeable finite length mode-III cracks in a functionally graded piezoelectric/piezomagnetic material plane. This problem is formulated into dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. In order to obtain the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials. The results show that the stress, the electric displacement, and the magnetic flux intensity factors of cracks depend on the crack length, the functionally graded parameter, and the distance among the multiple parallel cracks. The crack shielding effect is also obviously presented in a functionally graded piezoelectric/piezomagnetic material plane with multiple parallel symmetric mode-III cracks.

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Authors and Affiliations

  1. Center for Composite Materials and Structures, Harbin Institute of Technology, Harbin, 150080, P. R. China

    Shi-dong Pan  (泮世东), Zhen-gong Zhou  (周振功) & Lin-zhi Wu  (吴林志)

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  1. Shi-dong Pan  (泮世东)
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  2. Zhen-gong Zhou  (周振功)
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  3. Lin-zhi Wu  (吴林志)
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Correspondence to Shi-dong Pan  (泮世东).

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11002041 and 11272105), the Key Laboratory Opening Funding of Advanced Composites in Special Environment (No.HIT.KLOF.2009032), and the Research Fund for the Doctoral Program of Higher Education of China (No. 20092302110006)

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Pan, Sd., Zhou, Zg. & Wu, Lz. Basic solutions of multiple parallel symmetric mode-III cracks in functionally graded piezoelectric/piezomagnetic material plane. Appl. Math. Mech.-Engl. Ed. 34, 1201–1224 (2013). https://doi.org/10.1007/s10483-013-1739-6

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  • DOI: https://doi.org/10.1007/s10483-013-1739-6

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