The influence of third shear stress invariant dependence in the isotropic viscous relation on the reduced model for ice-sheet flow
Ice-sheet flow solutions commonly adopt a simple isotropic viscous law, in which the deviatoric stress is coaxial with the strain rate, and the single response function depends on only one invariant, the second principal invariant of the deviatoric stress. This can be correlated with single-stress c...
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ftuniveastangl:oai:ueaeprints.uea.ac.uk:52695 2023-05-15T16:40:18+02:00 The influence of third shear stress invariant dependence in the isotropic viscous relation on the reduced model for ice-sheet flow Morland, Leslie 2007-12-01 https://ueaeprints.uea.ac.uk/id/eprint/52695/ https://doi.org/10.3189/002214307784409289 unknown Morland, Leslie (2007) The influence of third shear stress invariant dependence in the isotropic viscous relation on the reduced model for ice-sheet flow. Journal of Glaciology, 53 (183). pp. 597-602. ISSN 0022-1430 doi:10.3189/002214307784409289 Article PeerReviewed 2007 ftuniveastangl https://doi.org/10.3189/002214307784409289 2023-02-09T23:31:17Z Ice-sheet flow solutions commonly adopt a simple isotropic viscous law, in which the deviatoric stress is coaxial with the strain rate, and the single response function depends on only one invariant, the second principal invariant of the deviatoric stress. This can be correlated with single-stress component tests, which cannot, however, verify the validity of the simplification. Morland (2007) has shown how combined compression and shear tests can verify and correlate a general quadratic isotropic viscous relation, or simply third invariant dependence, and there is evidence that at least third principal invariant dependence is required. Morland (2007) showed that a significant quadratic term changes the relative stress magnitudes in the reduced model for ice-sheet flow, that crucial simplifications are not achieved and formally noted that dependence on the third invariant in the coaxial relation also prevented the simplification. It is now shown that, provided the third invariant dependence does not dominate the isotropic relation, further asymptotic expansion does yield the reduced model simplification, and the influence of different weightings of third invariant dependence is illustrated by a comparison of steady radial flow solutions over a flat bed. It is found that the third invariant dependence does not have a large influence in these examples. Article in Journal/Newspaper Ice Sheet Journal of Glaciology University of East Anglia: UEA Digital Repository Journal of Glaciology 53 183 597 602 |
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University of East Anglia: UEA Digital Repository |
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Ice-sheet flow solutions commonly adopt a simple isotropic viscous law, in which the deviatoric stress is coaxial with the strain rate, and the single response function depends on only one invariant, the second principal invariant of the deviatoric stress. This can be correlated with single-stress component tests, which cannot, however, verify the validity of the simplification. Morland (2007) has shown how combined compression and shear tests can verify and correlate a general quadratic isotropic viscous relation, or simply third invariant dependence, and there is evidence that at least third principal invariant dependence is required. Morland (2007) showed that a significant quadratic term changes the relative stress magnitudes in the reduced model for ice-sheet flow, that crucial simplifications are not achieved and formally noted that dependence on the third invariant in the coaxial relation also prevented the simplification. It is now shown that, provided the third invariant dependence does not dominate the isotropic relation, further asymptotic expansion does yield the reduced model simplification, and the influence of different weightings of third invariant dependence is illustrated by a comparison of steady radial flow solutions over a flat bed. It is found that the third invariant dependence does not have a large influence in these examples. |
format |
Article in Journal/Newspaper |
author |
Morland, Leslie |
spellingShingle |
Morland, Leslie The influence of third shear stress invariant dependence in the isotropic viscous relation on the reduced model for ice-sheet flow |
author_facet |
Morland, Leslie |
author_sort |
Morland, Leslie |
title |
The influence of third shear stress invariant dependence in the isotropic viscous relation on the reduced model for ice-sheet flow |
title_short |
The influence of third shear stress invariant dependence in the isotropic viscous relation on the reduced model for ice-sheet flow |
title_full |
The influence of third shear stress invariant dependence in the isotropic viscous relation on the reduced model for ice-sheet flow |
title_fullStr |
The influence of third shear stress invariant dependence in the isotropic viscous relation on the reduced model for ice-sheet flow |
title_full_unstemmed |
The influence of third shear stress invariant dependence in the isotropic viscous relation on the reduced model for ice-sheet flow |
title_sort |
influence of third shear stress invariant dependence in the isotropic viscous relation on the reduced model for ice-sheet flow |
publishDate |
2007 |
url |
https://ueaeprints.uea.ac.uk/id/eprint/52695/ https://doi.org/10.3189/002214307784409289 |
genre |
Ice Sheet Journal of Glaciology |
genre_facet |
Ice Sheet Journal of Glaciology |
op_relation |
Morland, Leslie (2007) The influence of third shear stress invariant dependence in the isotropic viscous relation on the reduced model for ice-sheet flow. Journal of Glaciology, 53 (183). pp. 597-602. ISSN 0022-1430 doi:10.3189/002214307784409289 |
op_doi |
https://doi.org/10.3189/002214307784409289 |
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Journal of Glaciology |
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53 |
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183 |
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597 |
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602 |
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1766030683060305920 |