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

Abstract

Abstract 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.