On 3D problem of vertically uniform heat flow disturbed by an anticrack in a transversely isotropic magnetoelectroelastic space

The static equilibrium of a magnetoelectroelastic transversely isotropic space with a rigid sheet-like inclusion (an anticrack) of arbitrary shape in the isotropy plane under a remote normally incident uniform steady heat flow is studied. Considered is the case where the anticrack is thermally insulated and magnetoelectrically impermeable. By constructing appropriate harmonic potentials in the derived general solution, the governing two-dimensional singular integral equation is obtained in terms of a normal stress discontinuity across the inclusion. An analogy between the thermo-magnetoelectroelastic anticrack problem and its thermoelastic counterpart is exploited. A complete solution in terms of elementary functions is obtained and discussed in the simple case of a circular rigid disc-inclusion.