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Boundary integral equation method for conductive cracks in two and three-dimensional transversely isotropic piezoelectric media. (English) Zbl 1182.74245
Summary: Using the fundamental solutions and the Somigliana identity of piezoelectric medium, the boundary integral equations are obtained for a conductive planar crack of arbitrary shape in three-dimensional transversely isotropic piezoelectric medium. The singular behaviors near the crack edge are studied by boundary integral equation approach, and the intensity factors are derived in terms of the displacement discontinuity and the electric displacement boundary value sum near the crack edge on crack faces. The boundary integral equations for two dimensional crack problems are deduced as a special case of infinite strip planar crack. Based on the analogy of the obtained boundary integral equations and those for cracks in conventional isotropic elastic material and for contact problem of half-space under the action of a rigid punch, an analysis method is proposed. As an example, the solution to conductive Griffith crack is derived.

MSC:
74S15 Boundary element methods applied to problems in solid mechanics
74R10 Brittle fracture
74F15 Electromagnetic effects in solid mechanics
74E10 Anisotropy in solid mechanics
74G70 Stress concentrations, singularities in solid mechanics
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