An approximate statical solution of the elastoplastic interface for the problem of Galin with a cohesive-frictional material

An approximate statically admissible solution of the elastoplastic interface is described for the plane strain problem of a pressurized circular hole in a plane subject to a non-hydrostatic stress at infinity (Problem of Galin). In contrast to the solution of Galin (Prikl. Mat. Mekh.10, 365–386 (1946)) which applies for the case of a frictionless Tresca material, it is assumed that the material is characterized by a cohesivc-frictional yield strength. The solution of the elasloplastic interface is obtained in the form of a truncated series expansion, for cases where the material has yielded all around the hole. The paper discusses the limiting conditions for which the solution is applicable, and the validity of the solution in regard to an elastoplastic problem.