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Quasi-static cracks and minimal energy surfaces

V. I. Raisanen·E. T. Seppala·M. J. Alava·P. M. Duxbury
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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.

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V. I. Raisanen, E. T. Seppala, M. J. Alava, P. M. Duxbury. 1998-01-15. Quasi-static cracks and minimal energy surfaces. https://doi.org/10.1103/physrevlett.80.329

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