Quasistatic Cracks and Minimal Energy Surfaces

Abstract

We compare the roughness of minimal energy (ME) surfaces and scalar “quasistatic” fracture (SQF) surfaces. Two-dimensional ME and SQF surfaces have the same roughness scaling, w∼Lζ ( L is the system size) with ζ=23. The 3d ME and SQF results at strong disorder are consistent with the random-bond Ising exponent ζ(d≥3)≈0.21(5−d) ( d is the bulk dimension). However, 3d SQF surfaces are rougher than ME surfaces due to a larger prefactor. ME surfaces undergo a “weakly rough” to “algebraically rough” transition in 3d, suggesting a similar behavior in fracture.