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Emergent Anisotropy and Flow Alignment in Viscous Rock

This research focuses on the study of emergent anisotropy and flow alignment in viscous rock using a computational scheme. It includes investigations on folding instabilities in layered rock, viscoelastic lithosphere, chemical migration, and more. Publications and examples of flow alignment in simple shear and convection are provided.

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Emergent Anisotropy and Flow Alignment in Viscous Rock

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  1. Emergent Anisotropy and Flow Alignment in Viscous Rock by Hans Mühlhaus, Louis Moresi, Miroslav Cada May 5-10

  2. Outline • The last time…. (Hakone): Folding instabilities in layered rock using director theory combined with pressure solution, mobile and immobile phases, novel computational scheme • Publications: • - Louis Moresi, Frédéric Dufour, Hans Mühlhaus, Mantle convection models with viscoelastic/brittle lithosphere: Numerical methodology and plate tectonic modeling, PAGEOPH, submitted 2001 • -   Muhlhaus,H-B, Dufour,F, Moresi, L, Hobbs, BE (2001) A director theory for viscoelastic folding instabilities in multilayered rock (30 pages) submitted to the Int. J. Solids and Structures • -H-B Mühlhaus, L.N Moresi, B. Hobbs, and F. Dufour (2000)Large Amplitude Folding in Finely LayeredViscoelastic Rock Structures, PAGEOPH, submitted 2001 • -Hobbs, B.E., Muhlhaus,H-B, Ord, A and Moresi, L. (2000) The Influence of Chemical migration upon Fold Evolution in Multi-layered Materials. Vol. 11, Yearbook of Self Organisation. Eds H.J. Krug and J.H. Kruhl; Duncker&Humblot , Berlin , 229-252 • Today: Oriented materials and emergent anisotropy in simple shear and natural convection; thermal coupling in simple shear and …convection

  3. Finite Anisotropy Director evolution n : the director of the anisotropy W, Wn : spin and director spin D, D’: stretching and its deviatoric part

  4. Rotations average Spin of an infinitesimal volume element Spin of microstructure n n Undeformed ground state:

  5. Anisotropic Viscous Rheology If the director is oriented parallel x2: General case; n notparallel x2:

  6. Microstructures in Polycrystalline Materials during Deformation

  7. Moving integration points We interpolate the nodal velocities using the shape functions to update the particle positions. t is chosen “small” for accuracy purpose. The material history and stress rates are stored on particles.

  8. Orthotropic folding (click picture to play movie)

  9. Example 1

  10. Flow Alignment in Simple Shear

  11. …Nonlinear rheology, taken in the broadest sense, may be the single most important aspect of the behaviour of earth materials… Schubert, Karato, Olson, Turcotte From Outline of IMA Workshop Nonlin. Cont. Mech., Rheology and the Dynamo Extension with-and without yielding (click picture to play movie)

  12. Shear Histories simple shear and shear alignment with shear heating and temperature dependent viscosity

  13. Shear-Heating:Director Field andTemperature Contours

  14. Shear Alignment with Shear Heating and Temperature Dependent Viscosity

  15. Director Models Liquid Crystals: de Gennes & Prost, 1972, 1993 Geophysics: U Christensen, 1984 (post –glacial rebound, mantle convection) Director Evolution (U CH.): Transforms as line element Present Model: Transforms as surface normal vector

  16. Director ModelsSteady State The director evolution equation has a steady State solution in which the director is point-wise oriented normal to the velocity vectors. Solution maybe non-unique however……. Proof that is a particular solution for steady states:

  17. Stability of Normal Director SolutionRepresented are 2 solutions:One assuming director normal to velocity and one where the 1st 10 steps are run assuming normality and subsequent steps are integrated using full director evolution equation.

  18. Convection with Shear HeatingFull director evolution ; Di=0.25; Ra=1.2x106

  19. Director Alignment

  20. Degree of Alignment

  21. Director Alignment in ConvectionRa=0.5x106

  22. Conclusion • Rheology for layered materials as a basic unit (building stone) for more complex rheologies, modelling of crystallographic slip planes etc • director orthogonal to velocity vector in steady state • Orthogonal solution seems stable in convection • Mean shear strain of approx 6 required for alignment in simple shear • Examples include thermal coupling and influence thereof on alignment in simple shear, various convection studies • Codes used: Fastflo, Ellipsis www.ned.dem.csiro.au/research/solidmech

  23. Seismic Anisotropy

  24. Convection with Ra =500.000 Isotropy Anisotropy Stream function Isoterms Velocity Field

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