Fig. 1: Crack propagation in 3D and the linear 2D branching instability.

a A sketch of a 3D tensile crack experiment in a long bar of height L_y and thickness L_z. The long bar features a length L_x ≫ L_y, L_z, and only a small section of it is shown. The crack is located in the middle (symmetry) plane and will subsequently propagate predominantly in the x direction in response to a sufficiently large crack driving force G (related to the tensile loading, applied in the y direction). We employ periodic boundary conditions along the z direction (see “Methods”). The coordinates are normalized by the dissipation length ξ, see text for definition. b A linear crack branching instability in 2D, i.e., L_z = 0, occurring at a very high propagation velocity v_B = 0.95c_R (c_R is the Rayleigh wave-speed), once a threshold tensile driving force G_B is surpassed. See text and Fig. 2 for additional discussion.