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Singularity analysis of planar cracks in three-dimensional piezoelectric semiconductors via extended displacement discontinuity boundary integral equation method. (English) Zbl 1403.74266
Summary: The displacement discontinuity boundary integral equation method is extended to analyze the singularity of near-border fields of the planar crack of arbitrary shape in the isotropic plane of a three-dimensional transversely isotropic piezoelectric semiconductor. The hyper-singular boundary integral equations are derived in terms of the displacement, electric potential and carrier density discontinuities across the crack faces, in which body integrals for the carrier density are introduced. Based on the finite-part integrals, singularity exponents and asymptotic expressions of the crack border fields are obtained. The stress, electric displacement and electric current intensity factors are given in terms of the displacement, electric potential and carrier density discontinuities. Finite element results for penny-shaped and line cracks based on the piezoelectric-conductor iterative method are used to verify the derivations of the intensity factors.

74S15 Boundary element methods applied to problems in solid mechanics
65N38 Boundary element methods for boundary value problems involving PDEs
74F15 Electromagnetic effects in solid mechanics
74R10 Brittle fracture
Full Text: DOI
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