Abstract
The near-tip fields of an anti-plane crack in functionally graded piezoelectric materials (FGPMs) are investigated. To make the analysis tractable as usual, the elastic stiffness, piezoelectric parameter, and dielectric permittivity of FGPMs are assumed to be exponential functions of x parallel to the crack. The boundary conditions on crack surfaces are assumed to be the stress free and electrically impermeable. The high order crack tip stress and electric displacement fields are obtained by the eigen-expansion method. This study possesses fundamental significance as Williams’ solution to homogeneous materials.
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