FRACTURE ROUGHNESS FOR THE TWO-DIMENSIONAL CENTRAL FORCE MODEL

We study the fracture roughness for a two-dimensional central force model by nu-merical simulations to check the conjecture that the fracture roughness is due to the fracture process being a stress-weighted percolation process. The simulations are done on a triangular lattice and the fracture process is quasi-static. The simulations are done in mode I and the elastic equilibrium equations are solved with the iterative con-jugated gradient method. The material has non-uniform material properties through disorder in the breaking thresholds for the bonds on the lattice. We find that for small disorders in the breaking thresholds the fracture is localised and the fracture roughness is found to be ζ = 0.70 ± 0.05. We also measure the percolation correlation length exponent for large disorders and find ν = 1.43 ± 0.10, which suggests that the value of ζ is in the upper part of the interval. The result for ν also excludes generic rigid-ity percolation as the universality class of the stress weighted percolation process in this model. In the infinite disorder limit the gradient imposed on the damage distribu-tion by the fracture process makes this model different from ordinary rigid percolation.