Induced anisotropy in large ice shields: theory and its homogenization

Gödert, Günter; Hutter, Kolumban

doi:10.1007/s001610050095

Cited by 56 publications

(62 citation statements)

References 19 publications

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“…One can also see the importance of compaction in the dynamics of large ice masses as mentioned by Gödert et al in [13].…”

Section: Introductionmentioning

confidence: 74%

“…We denote (σ 1 , p 1 , v 1 ) and (σ 2 , p 2 , v 2 ) two solutions to system (13,16,15) with the boundary conditions (9)- (11) and (12).…”

Section: Presentation Of the Duality Methodsmentioning

confidence: 99%

“…In Section 4, we present the mathematical analysis of the first iteration of (13,14) and (15) in the case of a predictive-corrective type discretisation. General amplitude compaction is considered.…”

Section: Presentation Of the System Of Equationsmentioning

confidence: 99%

“…Definition of a solution Definition 3.1. One calls solution to System (13,16,15) for Conditions (9)- (11) and (12), (13) and (16) are satisfied a.e. in Ω, and, for any ϕ in V 0 ,…”

Section: Hypothesismentioning

confidence: 99%

“…It is immediate to notice that the solutions of System (13,16,15), for the boundary conditions (9)-(11) and the interface condition (12), are the fixed points of S.…”

Section: Existence Of a Solutionmentioning

confidence: 99%

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Vertical compaction in a faulted sedimentary basin

Gagneux¹,

Masson²,

Plouvier-Debaigt³

et al. 2003

ESAIM: M2AN

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Abstract.In this paper, we consider a 2D mathematical modelling of the vertical compaction effect in a water saturated sedimentary basin. This model is described by the usual conservation laws, Darcy's law, the porosity as a function of the vertical component of the effective stress and the Kozeny-Carman tensor, taking into account fracturation effects. This model leads to study the time discretization of a nonlinear system of partial differential equations. The existence is obtained by a fixed-point argument. The uniqueness proof, by Holmgren's method, leads to work out a linear, strongly coupled, system of partial differential equations and boundary conditions. Mathematics Subject Classification. 35Q35, 76S05, 35J65.

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“…One can also see the importance of compaction in the dynamics of large ice masses as mentioned by Gödert et al in [13].…”

Section: Introductionmentioning

confidence: 74%

“…We denote (σ 1 , p 1 , v 1 ) and (σ 2 , p 2 , v 2 ) two solutions to system (13,16,15) with the boundary conditions (9)- (11) and (12).…”

Section: Presentation Of the Duality Methodsmentioning

confidence: 99%

Section: Presentation Of the System Of Equationsmentioning

confidence: 99%

“…Definition of a solution Definition 3.1. One calls solution to System (13,16,15) for Conditions (9)- (11) and (12), (13) and (16) are satisfied a.e. in Ω, and, for any ϕ in V 0 ,…”

Section: Hypothesismentioning

confidence: 99%

“…It is immediate to notice that the solutions of System (13,16,15), for the boundary conditions (9)-(11) and the interface condition (12), are the fixed points of S.…”

Section: Existence Of a Solutionmentioning

confidence: 99%

See 3 more Smart Citations

Vertical compaction in a faulted sedimentary basin

Gagneux¹,

Masson²,

Plouvier-Debaigt³

et al. 2003

ESAIM: M2AN

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A Critical Review of the Mechanics of Polycrystalline Polar Ice

Placidi¹,

Hutter

Faria

2006

GAMM-Mitteilungen

Self Cite

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We review the developments of the constitutive theories of polar ice both from a viewpoint of mechanics as well as materials science, as it was studied during the last approximately 50 years. First proposals were based on the postulation of ice as a very viscous, non-Newtonian and heat conducting fluid. Today's understanding of polar ice sees it as a creeping polycrystal with induced anisotropy and a nontrivial grain-size distribution, both evolving in time. Phenomena related to recrystallization, namely grain rotation, grain-size redistribution by normal and abnormal grain growth, nucleation, polygonization and grain boundary migration have also to be accounted for to obtain a stress constitutive law that may reliably predict ice flow in large ice masses. The main topics on which we focus our efforts are the role of anisotropy and its evolution. We review the models that take into account the microscopic as well as the macroscopic point of view. Numerical models are also considered. A novel graphical method is proposed for the comprehension of the rules that drive the rotation of the crystallites in a polycrystal, not only for the simple cases of compression and extension but also for the simple shear mode of deformation. Particular emphasis is given to the constitutive theories related to recrystallization phenomena, for which the paper can be considered an introductory overview. The research methods on which all proposed laws are based borrow concepts from the mechanics of solids and materials science but belong also to the class of anisotropic fluids.

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Computational modeling of flow‐induced anisotropy of polar ice for the EDML deep drilling site, Antarctica: The effect of rotation recrystallization and grain boundary migration

Bargmann

Seddik

Greve

2011

Num Anal Meth Geomechanics

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SUMMARYIn this contribution we model flow-induced anisotropy of polar ice in order to gain a better understanding for the underlying microstructure and its influence on the deformation process. In particular, a continuummechanical, anisotropic flow model that is based on an anisotropic flow enhancement factor (CAFFE model) is applied. The polycrystalline ice is regarded as a mixture whose grains are characterized by their orientation. The approach is based on two distinct scales: the underlying microstructure influences the macroscopic material behavior and is taken into account phenomenologically. To achieve this, the orientation mass density is introduced as a mesoscopic field, i.e. it depends on a mesoscopic variable (the orientation) in addition to position and time. The classical flow law of Glen is extended by a scalar, but anisotropic enhancement factor. Four different effects (local rigid body rotation, grain rotation, rotation recrystallization, grain boundary migration) influencing the evolution of the grain orientations are taken into account. All modeling parameters are either measurable in or derivable from field observations or laboratory experiments. A finite volume method is chosen for the discretization procedure. Numerical results simulating the ice flow at the site of the EPICA ice core in Dronning Maud Land (referred to as EDML), Antarctica, are presented. They go beyond earlier results by Seddik et al. (J. Glaciol. 2008; 54(187):631-642) in which only local rigid body rotation and grain rotation were accounted for. By comparing simulated and observed fabrics, we come up with reference values for the parameters in the constitutive equations for rotation recrystallization and grain boundary migration. Down to 2045 m depth, good agreement can be achieved; however, further down the observed fabric cannot be reproduced well due to numerical issues. Additionally, we study the influence of the two superposed deformation regimes of vertical compression and simple shear separately and demonstrate that the numerical problems are due to the predominant shear regime near the bottom, whereas vertical compression only produces stable results everywhere.

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Induced anisotropy in large ice shields: theory and its homogenization

Cited by 56 publications

References 19 publications

Vertical compaction in a faulted sedimentary basin

Vertical compaction in a faulted sedimentary basin

A Critical Review of the Mechanics of Polycrystalline Polar Ice

Computational modeling of flow‐induced anisotropy of polar ice for the EDML deep drilling site, Antarctica: The effect of rotation recrystallization and grain boundary migration

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