An algorithm for simulating fracture of cohesive–frictional materials

Fracture of disordered frictional granular materials is dominated by interfacial failure response that is characterized by de-cohesion followed by frictional sliding response. To capture such an interfacial failure response, we introduce a cohesive–friction random fuse model (CFRFM), wherein the cohesive response of the interface is represented by a linear stress–strain response until a failure threshold, which is then followed by a constant response at a threshold lower than the initial failure threshold to represent the interfacial frictional sliding mechanism. This paper presents an efficient algorithm for simulating fracture of such disordered frictional granular materials using the CFRFM. We note that, when applied to perfectly plastic disordered materials, our algorithm is both theoretically and numerically equivalent to the traditional tangent algorithm (Roux and Hansen 1992 J. Physique II 2 1007) used for such simulations. However, the algorithm is general and is capable of modeling discontinuous interfacial response. Our numerical simulations using the algorithm indicate that the local and global roughness exponents (ζloc and ζ, respectively) of the fracture surface are equal to each other, and the two-dimensional crack roughness exponent is estimated to be ζloc = ζ = 0.69 ± 0.03