Quasistatic Cracks and Minimal Energy Surfaces

V.I. Räisänen; E.T. Seppälä; M.J. Alava; P.M. Duxbury

doi:10.1103/PhysRevLett.80.329

Quasistatic Cracks and Minimal Energy Surfaces

V.I. Räisänen, E.T. Seppälä, M.J. Alava, P.M. Duxbury

Department of Applied Physics

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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.

Original language	English
Pages (from-to)	329-332
Journal	Physical Review Letters
Volume	80
Issue number	2
DOIs	https://doi.org/10.1103/PhysRevLett.80.329
Publication status	Published - 1998
MoE publication type	A1 Journal article-refereed

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title = "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.",

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AU - Räisänen, V.I.

AU - Seppälä, E.T.

AU - Alava, M.J.

AU - Duxbury, P.M.

PY - 1998

Y1 - 1998

N2 - 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.

AB - 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.

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SP - 329

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JO - Physical Review Letters

JF - Physical Review Letters

IS - 2

ER -

Quasistatic Cracks and Minimal Energy Surfaces

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