We perform an elastostatic analysis of a periodic array of cracks under constant loading. We give an analytical solution and show that there is a limitation to the fracture spacing, due to a transition from an opening to a compressive loading. For this configuration, the threshold of the fracture spacing depends on neither the applied strain nor the elastic parameters of the material. This result shows that, in the general case of layered materials, the physical mechanism that is responsible for the limitation in the density of fractures is related mainly to the geometry of the problem. This is in agreement with observations and with recent numerical results.

• Received 18 November 2000

DOI:https://doi.org/10.1103/PhysRevLett.86.5703