On 3D problem of an anticrack under vertically uniform heat flow in a transversely isotropic electro-thermo-elastic space

A static thermoelectroelastic problem for a transversely isotropic space with an arbitrary shaped rigid sheet-like inclusion (an anticrack) in the isotropy plane obstructing a uniform steady heat flow is investigated. The anticrack is treated as isothermal and electrically impermeable. A general method of solving the resulting boundary-value problems is presented. Using the derived general solution and the generalized potential theory method, the governing two-dimensional singular integral equation is obtained in terms of a normal stress discontinuity across the inclusion. An analogy between the thermoelectromechanical anticrack problem and its thermomechanical counterpart is exploited. As an illustration, a typical application to a circular rigid disc-inclusion is presented. In this case a complete solution in elementary functions is achievable. Explicit expressions for the thermoelectrostressed state in the inclusion plane are given and discussed from the point of view of material failure. (C) 2017 Elsevier Masson SAS. All rights reserved.