Simulation of extensional clay fractures

A spring network model has been used to study fractures in thin layers of material supported by a deformable substrate. The interactions with the substrate localize the stress/strain field in the material. The crossover of the shape of a single fracture in an ordered material from an elliptical form to a long, thin shape was studied as a function of the substrate attachment strength. For many interacting fractures in a disordered material, the simulated fracture patterns reproduced the most important visual and statistical properties of fracture patterns from recent experiments on thin slabs of clay attached to a deformable substrate. In particular, the correspondence was good for a new set of scaling relations between the lengths and areas of fractures. The shapes of the larger cracks were consistent with a self-affine curve with a Hurst exponent of $0.5.$ The dynamics of the development of the fracture pattern corresponds qualitatively to experimental results.