Continuum Mechanics and Thermodynamics

, Volume 22, Issue 3, pp 221–237 | Cite as

Continuum-mechanical, Anisotropic Flow model for polar ice masses, based on an anisotropic Flow Enhancement factor

  • Luca Placidi
  • Ralf Greve
  • Hakime Seddik
  • Sérgio H. Faria
Open Access
Original Article


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.


Continuum 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).

Open Access

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.


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Copyright information

© The Author(s) 2009

Authors and Affiliations

  • Luca Placidi
    • 1
    • 2
  • Ralf Greve
    • 3
  • Hakime Seddik
    • 3
  • Sérgio H. Faria
    • 4
  1. 1.Department of Structural and Geotechnical Engineering“Sapienza”, University of RomeRomeItaly
  2. 2.Smart Materials and Structures LaboratoryCisterna di LatinaItaly
  3. 3.Institute of Low Temperature ScienceHokkaido UniversitySapporoJapan
  4. 4.GZG, Department of CrystallographyUniversity of GöttingenGöttingenGermany

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