Exact results with the <i>J</i>-integral applied 
to free-boundary flows

Amar, Martine Ben; Rice, James R.

doi:10.1017/s0022112002008418

Cited by 14 publications

(5 citation statements)

References 49 publications

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“…Cherepanov [1968], and Bilby and Eshelby [1968] in the context of cracks in elastic solids but have been generalized to more complex, nonlinear creep rheologies [e.g., Goldman and Hutchinson, 1975;Landes and Begley, 1976;Kubo et al, 1979;Ben Amar and Rice, 2002] relevant for our case and applied to glaciers by McMeeking and Johnson [1986].…”

Section: 1002/2013jf003008mentioning

confidence: 99%

Deformation-induced melting in the margins of the West Antarctic ice streams

Suckale

Platt

Perol

et al. 2014

J. Geophys. Res. Earth Surf.

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127

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Flow of glacial ice in the West Antarctic Ice Sheet localizes in narrow bands of fast‐flowing ice streams bordered by ridges of nearly stagnant ice, but our understanding of the physical processes that generate this morphology is incomplete. Here we study the thermal and mechanical properties of ice‐stream margins, where flow transitions from rapid to stagnant over a few kilometers. Our goal is to explore under which conditions the intense shear deformation in the margin may lead to deformation‐induced melting. We propose a 2‐D model that represents a cross section through the ice stream margin perpendicular to the downstream flow direction. We limit temperature to the melting point to estimate melt rates based on latent heat. Using rheology parameters as constrained by laboratory data and observations, we conclude that a zone of temperate ice is likely to form in active shear margins.

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Section: 1002/2013jf003008mentioning

confidence: 99%

Deformation-induced melting in the margins of the West Antarctic ice streams

Suckale

Platt

Perol

et al. 2014

J. Geophys. Res. Earth Surf.

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127

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“…A simple force balance for the ice stream shows that τ lat is the average lateral drag supported by the shear margin. The path‐independent integral in Suckale et al [] is an extension of the J ‐type integrals first introduced for cracks in elastic solids by Rice [], Cherepanov [], and Bilby and Eshelby [], later generalized to the nonlinear creep rheologies we consider [e.g., Goldman and Hutchinson , ; Landes and Begley , ; Kubo et al , ; Ben Amar and Rice , ] and previously applied to glaciers by McMeeking and Johnson []. Inserting equation into equation we find

τ_{sharp} = τ_{lat} {((), \frac{4 Hn}{{(n + 1)}^{2} πy})}^{1 / (n + 1)} .

…”

Section: Deformation Around a Sharp Transitionmentioning

confidence: 99%

Determining conditions that allow a shear margin to coincide with a Röthlisberger channel

et al. 2016

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The mass loss from the West Antarctic Ice Sheet is dominated by numerous rapidly flowing ice streams, which are separated from stagnant ice in the adjacent ridges by zones of concentrated deformation known as shear margins. Because the discharge from a single ice stream depends sensitively on the ice stream width, determining the physical processes that control shear margin location is crucial to a full understanding of ice stream dynamics. Previous work has shown that the transition from a deforming to an undeforming bed within a shear margin concentrates large stresses on the undeforming bed beneath the ridge. In this paper we investigate how the presence of a drainage channel collocated with the transition from a deforming to an undeforming bed perturbs the stress field within the shear margin. We show that the channel limits the maximum shear stress on the undeforming bed and alters the yield strength of the till by changing the normal stress on the ice‐till interface. By comparing the maximum stress with the till strength, we show that the transition from a deforming to an undeforming bed can occur across a channel whenever the water flux in the channel exceeds a critical value. This critical flux is sensitive to the rheology and loading of the shear margin, but we conclude that there are some scenarios where the transition from a deforming to an undeforming bed can be collocated with a drainage channel, though this configuration is probably not typical.

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“…Pseudo-momentum has been widely considered in fluids, e.g. Ben Amar and Rice [ 18 ] showed the analogy in the application of the J integral between a screw dislocation and a vortex line, while the pseudo-momentum of a disturbance has been used in obtaining instabilities in sheared fluid interfaces (e.g. Eaves and Balmforth [ 19 ]).…”

Section: Discussionmentioning

confidence: 99%

Loss of pseudo-momentum, energy-release rate and the effective mass of a moving dislocation

Markenscoff

2023

Phil. Trans. R. Soc. A.

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In a seminal paper in the Philosophical Transactions of the Royal Society (A244, 87–112). Eshelby (Eshelby 1951 Phil. Trans. R. Soc. Lond. A 244, 87–112. ( doi:10.1098/rsta.1951.0016 )) introduced the concept of ‘the force on an elastic singularity’ and suggested that the extensions to dynamics include the application of the momentum flux. In this direction, it is shown that, in the non-uniformly motion of a dislocation there is a loss in quasi-momentum (or pseudo-momentum) across the scales ε to ε 2 , which induces an effective mass of the dislocation, and a loss in kinetic energy across the scales. It is shown through Noether's theorem that the rate of change of quasi-momentum in the volume enclosing the dislocation is equal to the flux of it through the surface minus a quasi-force, which is the dynamic J integral. The connection between the variation in the Hamiltonian and in the Lagrangian relates the quasi-force to the energy-release rate, yielding the same effective mass, while providing physical meaning both through momentum and energy. The effective mass of a dislocation is important in relating the energetics of defects from the micro to the macro scales, and the loss of quasi-momentum can have wider applications in continua. This article is part of the theme issue 'Foundational issues, analysis and geometry in continuum mechanics'.

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Exact results with the J-integral applied to free-boundary flows

Cited by 14 publications

References 49 publications

Deformation-induced melting in the margins of the West Antarctic ice streams

Deformation-induced melting in the margins of the West Antarctic ice streams

Determining conditions that allow a shear margin to coincide with a Röthlisberger channel

Loss of pseudo-momentum, energy-release rate and the effective mass of a moving dislocation

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