Coplanar propagation paths of 3D cracks in infinite bodies loaded in shear

Bower and Ortiz, recently followed by Lazarus, developed a powerful method, based on a theoretical work of Rice, for numerical simulation of planar propagation paths of mode 1 cracks in infinite isotropic elastic bodies. The efficiency of this method arose from the need for the sole 1D meshing of the crack front. This paper presents an extension of Rice's theoretical work and the associated numerical scheme to mixed-mode (2 + 3) shear loadings. Propagation is supposed to be channeled along some weak planar layer and to remain therefore coplanar, as in the case of a geological fault for instance. The capabilities of the method are illustrated by computing the propagation paths of cracks with various initial contours (circular, elliptic, rectangular, heart-shaped) in both fatigue and brittle fracture. The crack quickly reaches a stable, almost elliptic shape in all cases. An approximate but accurate analytic formula for the ratio of the axes of this stable shape is derived.