Influence of heterogeneities on crack propagation

The influence of material heterogeneities is studied in the context of dynamic failure. We consider a pre-strained plate problem, the homogeneous case of which has been widely studied both experimentally and numerically. This setup is used to isolate the effects of the elastic field resulting from pre-straining and stress wave interactions throughout the crack propagation by adding stiffer and denser regions in the plate. While the crack tip is pushed away by stiffer inclusions, it is attracted to the denser ones. With the presence of denser media, only a portion of the total elastic energy in the system is effectively used to drive crack propagation, leading to a drop in the velocity of its tip in comparison to the homogeneous case. Crack branching is then observed at velocities much lower than the limiting velocity of the material, questioning the validity of crack velocity to be a criterion for crack branching. Instead, we introduce an effective stored energy to analyze the crack velocity and the emergence of crack branching instabilities.