Quasi-static cracks and minimal energy surfaces

TL;DR

This paper compares the roughness of minimal energy surfaces and quasi-static fracture surfaces across dimensions, revealing similar scaling in 2D and consistent behavior in 3D with some differences, indicating potential transitions in roughness regimes.

Contribution

It provides a comparative analysis of ME and SQF surface roughness, highlighting their scaling similarities and differences across dimensions, and suggests a transition in 3D roughness behavior.

Findings

2D ME and SQF surfaces have the same roughness scaling with zeta=2/3.

3D ME and SQF surfaces at strong disorder are consistent with the random-bond Ising exponent.

3D SQF surfaces are rougher than ME surfaces due to a larger prefactor.

Abstract

We compare the roughness of minimal energy(ME) surfaces and scalar ``quasi-static'' fracture surfaces(SQF). Two dimensional ME and SQF surfaces have the same roughness scaling, w sim L^zeta (L is system size) with zeta = 2/3. The 3-d ME and SQF results at strong disorder are consistent with the random-bond Ising exponent zeta (d >= 3) approx 0.21(5-d) (d is bulk dimension). However 3-d SQF surfaces are rougher than ME ones due to a larger prefactor. ME surfaces undergo a ``weakly rough'' to ``algebraically rough'' transition in 3-d, suggesting a similar behavior in fracture.