Continuum-mechanical, Anisotropic Flow model for polar ice masses, based on an anisotropic Flow Enhancement factor
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A complete theoretical presentation of the Continuum-mechanical, Anisotropic Flow model, based on an anisotropic Flow Enhancement factor (CAFFE model) is given. The CAFFE model is an application of the theory of mixtures with continuous diversity for the case of large polar ice masses in which induced anisotropy occurs. The anisotropic response of the polycrystalline ice is described by a generalization of Glen’s flow law, based on a scalar anisotropic enhancement factor. The enhancement factor depends on the orientation mass density, which is closely related to the orientation distribution function and describes the distribution of grain orientations (fabric). Fabric evolution is governed by the orientation mass balance, which depends on four distinct effects, interpreted as local rigid body rotation, grain rotation, rotation recrystallization (polygonization) and grain boundary migration (migration recrystallization), respectively. It is proven that the flow law of the CAFFE model is truly anisotropic despite the collinearity between the stress deviator and stretching tensors.
KeywordsContinuum mechanics Anisotropy Ice Mixtures Recrystallization
The authors would like to thank Kolumban Hutter and Leslie W. Morland for many productive discussions. Comments of the scientific editor Wolfgang Müller and an anonymous reviewer helped considerably to improve the structure and clarity of the manuscript. This study was supported by a Grant-in-Aid for Creative Scientific Research (No. 14GS0202) from the Japanese Ministry of Education, Culture, Sports, Science and Technology, by a Grant-in-Aid for Scientific Research (No. 18340135) from the Japan Society for the Promotion of Science, and by a grant (Nr. FA 840/1-1) from the Priority Program SPP-1158 of the Deutsche Forschungsgemeinschaft (DFG).
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
- 15.Gagliardini O., Gillet-Chaulet F., Montagnat M.: A review of anisotropic polar ice models: from crystal to ice-sheet flow models. In: Hondoh, T. (eds) Physics of Ice Core Records, vol. 2, Yoshioka Publishing, Kyoto, Japan (2009)Google Scholar
- 20.Hutter K.: Theoretical Glaciology: Material Science of Ice and the Mechanics of Glaciers and Ice Sheets. D Reidel Publishing Company, Dordrecht, The Netherlands (1983)Google Scholar
- 22.Kamb B.: Experimental recrystallization of ice under stress. In: Heard, H.C., Borg, I.Y., Carter, N.L., Raileigh, C.B. (eds) Flow and Fracture of Rocks, pp. 211–241. American Geophysical Union, Washington, DC (1972)Google Scholar
- 23.Larson R.G.: Constitutive Equations for Polymer Melts and Solutions. Butterworths Series in Chemical Engineering. Butterworths, Boston (1988)Google Scholar
- 24.Larson R.G.: The Structure and Rheology of Complex Fluids. Oxford University press, Oxford (1999)Google Scholar
- 29.McConnel J.C.: On the plasticity of an ice crystal. Proc. R. Soc. Lond. 49, 323–343 (1891)Google Scholar
- 30.Miyamoto A.: Mechanical properties and crystal textures of Greenland deep ice cores. Doctoral thesis. Hokkaido University, Sapporo Japan (1999)Google Scholar
- 37.Paterson W.S.B.: The Physics of Glaciers. 3rd edn. Pergamon Press, Oxford (1994)Google Scholar
- 38.Pimienta P., Duval P., Lipenkov V.Y.: Mechanical behaviour of anisotropic polar ice. In: Waddington, E.D., Walder, J.S. (eds) The Physical Basis of Ice Sheet Modelling, pp. 57–66. IAHS Publication IAHS Press, Wallingford, UK (1987)Google Scholar
- 39.Placidi, L.: Thermodynamically consistent formulation of induced anisotropy in polar ice accounting for grain-rotation, grain-size evolution and recrystallization. Doctoral thesis, Department of Mechanics, Darmstadt University of Technology, German (2004). Available at http://elib.tu-darmstadt.de/diss/000614/
- 40.Placidi L.: Microstructured continua treated by the theory of mixtures. Doctoral thesis. University of Rome, La Sapienza, Italy (2005)Google Scholar
- 42.Placidi, L., Hutter, K.: Characteristics of orientation and grain-size distributions. In: Proceedings of the 21st International Congress of Theoretical and Applied Mechanics. Warsaw, Poland (2004)Google Scholar
- 48.Seddik, H.: A full-Stokes finite-element model for the vicinity of Dome Fuji with flow-induced anisotropy and fabric evolution. Doctoral thesis, Graduate School of Environmental Science, Hokkaido University, Sapporo, Japan (2008). Available at http://hdl.handle.net/2115/34136
- 55.Truesdell C.: Sulle basi della termomeccanica, Nota II. Rendiconnti Accademia dei Lincei 8/22, 158–166 (1957b)Google Scholar