On 3D anticrack problems in a transversely isotropic solid

•The 3D anticrack problem in a transversely isotropic space is examined.•The potential function method is applied.•The 2D singular integral equations for the stress jump functions are derived.•Solution for a circular anticrack under triaxial loads is given and discussed.

Three-dimensional analysis is performed for an infinitive transversely isotropic elastic body containing a rigid sheet-like inclusion (anticrack) in the isotropy plane under some external mechanical loads. Effective results have been achieved by constructing the suitable potential solutions and reducing the resulting boundary-value problems to mixed problems of the potential theory. The governing boundary integral equations for a planar anticrack of arbitrary shape are obtained with the unknown stress jumps across the inclusion. A complete solution in elementary functions is given and discussed for a circular rigid disc-inclusion in an otherwise uniform tensile field.