A novel approach to calculate the KIII factor for a crack on a sharp corner using Green's function

•Green’s function is determined for calculating the KIII factor for a crack.•A new approach which uses FEM to find Green’s function is proposed.•Numerical results were validated by comparison to exact values according to Sih.•Results show that the estimation error is acceptably small (%3). This paper presents a method for determining Green's function for calculating the KIII factor for a crack initiated at the vertex of a sharp corner and coming out at different angles when the crack length is small compared to other element dimensions. A new approach to find a Green's function by means of FEM for symmetric problems and adapting it for non-symmetric problems has been applied, using the hypothesis of free released energy in combination with a special technique of building non-symmetric shapes from symmetric elements. This approach obtained approximate solutions, so special emphasis was placed on estimating the error of the obtained solutions. It was found that the high precision of the obtained Green's function is sufficient for practical use in calculating the durability and strength of structural elements under an anti-plane strain state.