Dugdale model applied to a mixed mode loading of a semi infinite cracked structure

The Dugdale model was initially developed in the case of {a} mode I loading. It was extended to other modes and to {the} mixed mode case. The exact solutions were given for all these modes in the case of an infinite medium with a straight crack. This work is an application of the Dugdale model to a crack in a semi infinite structure submitted to a mixed mode loading. The coupled system of singular integral equations of the first kind corresponding to the {elastostatic} problem is solved semi-analytically. Particular attention is needed in the resolution because of jump discontinuities in the loading of the crack faces. The criteria of propagation are deduced {from} the revisited Griffith theory (G. Francfort, J-J. Marigo, Journal of Mechanics and Physics of Solids(1998) 46:8 1319-1342). The presented results show the evolution of the {applied load and critical stress with the crack length}. {The shape of the crack gap is also presented}. A comparison with the problem of a crack in an infinite structure is performe