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Penny-shaped crack in transversely isotropic piezoelectric materials. (English) Zbl 0817.73052
The author presents two forms of the generalized static solutions describing the electromechanical behavior of a transversely isotropic piezoelectric continuum in the cylindrical coordinates. The general three-dimensional axisymmetric solutions are reduced to finding either one function of higher order or three quasi-harmonic functions. Then, a penny-shaped crack embedded in the piezoelectric continuum is investigated under axisymmetric static tensile load. The Fourier-Hankel transformation is used. The crack-tip stress field and the electric displacement field are obtained. The results presented can be readily used to solve the penny-shaped crack under radial shear loading. The paper may appeal to researchers interested in the fracture of piezoelectric materials.

74F15 Electromagnetic effects in solid mechanics
76M25 Other numerical methods (fluid mechanics) (MSC2010)
Full Text: DOI
[1] Deeg WF. The analysis of dislocation, crack, and inclusion problems in piezoelectric solids. PhD Thesis, Stanford University, 1980
[2] Pak YE. Crack extension force in a piezoelectric material.J Appl Mech, 1992, 57(3): 647–653 · Zbl 0724.73191 · doi:10.1115/1.2897071
[3] Sosa HA and Pak YE. Three-dimensional eigenfunction analysis of a crack in a piezoelectric material.Int J Solids Structures, 1990, 26(1): 1–15 · Zbl 0707.73064 · doi:10.1016/0020-7683(90)90090-I
[4] Senddon IN, Fourier Transforms. New York: McGraw-Hill, 1951
[5] Senddon IN and Lowengrub M. Crack Problems in the Classical Theory of Elasticity. New York: John Wiley and Sons, 1969
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