HR: 10:20h
AN: T12B-01 INVITED    [Abstracts]
TI: Anisotropic Visco-Plastic Deformations in Geodynamics: Folding, Shear Banding and Mantle Convection
AU: * Muhlhaus, H B
EM: muhlhaus@esscc.uq.edu.au
AF: The University of Queensland, ESSCC, Sir James Foots Bulding(47a), Brisbane, QLD 4072, Australia
AU: Moresi, L
EM: louis.moresi@sci.monash.edu.au
AF: Monash University, School of Mathematical Sciences, Building 28, Clayton, VIC 3800, Australia
AB: We give an outline of a constitutive relationship for transversely isotropic elastic-viscous materials. The formulation intended for materials with fine internal layering, which can be described by a single director orientation. This constitutive model is specifically designed for geological deformation problems involving very large deformations. Although there are more general descriptions possible, this formulation is, in fact, very broadly applicable to crustal rocks, where the preponderance of layering arises from deposition of one rock type onto another under gravity. We revisit the basic finite element formulation for viscous materials and demonstrate how the standard element vectors and matrices can be extended to include anisotropy. We explore scenarios from global to internal buckling in nonlinear finite element studies. These show that buckling can be induced at much lower viscosity contrasts between the matrix and the embedded beam or plate than would be the case for isotropic materials. Numerical solutions based on the standard continuum formulation assumed initially may become unstable if the contrast between the normal - and the shear viscosity becomes very severe. The director formulation can also be used to define a prefered plane for slip to occur given the local stress field. The simple-shear viscosity and the deformation can then be iterated to ensure that the yield criterion is always satisfied. We assume the Boussinesq approximation, neglecting any effect of dilatancy on the stress field. An additional criterion is required to ensure that deformation occurs along the plane aligned with maximum shear strain-rate rather than the perpendicular plane, which is formally equivalent in any symmetric formulation. Here we also allow for strain-weakening of the material. The material can remember both the accumulated failure history and the direction of failure. We have included this capacity in a Lagrangian-integration-point finite element code and show a number of examples of extension and compression of a crustal block with a Mohr–Coulomb failure criterion. The formulation itself is general and applies to 2-and 3-dimensional problems.
DE: 1236 Rheology of the lithosphere and mantle (7218, 8160)
DE: 8032 Rheology: general (8160)
DE: 8108 Continental tectonics: compressional
DE: 8168 Stresses: general
SC: Tectonophysics [T]
MN: 2007 Fall Meeting