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Green’s functions for anti-plane deformations of a circular arc-crack at the interface of piezoelectric materials. (English) Zbl 1063.74092

Summary: The anti-plane deformation problem of an interfacial debounding crack between a circular piezoelectric inclusion and a piezoelectric matrix is investigated by means of the complex variable method. For a line load applied within the matrix or inside the inclusion, Green’s functions are presented for the complex potentials, intensity factors and electric fields on the crack faces, respectively, in closed and explicit form. The solutions are valid for both permeable and impermeable crack models. It is shown that, in the general case of permeable cracks, the electric field singularity is always proportional to the stress singularity.

MSC:

74R10 Brittle fracture
74F15 Electromagnetic effects in solid mechanics
74G70 Stress concentrations, singularities in solid mechanics
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