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Conference Papers Year : 2001

Buckling and flow alignment in foliated rock


A model for finely layered visco-elastic rock proposed by us in previous papers is used as the basic unit for a granular rock. The grains are distinguished by individual layer orientations. Initially the layer orientations are randomly distributed. Size effects are considered within the framework of a couple stress theory. We begin with an outline of the governing equations for the standard continuum case and apply a computational simulation scheme suitable for problems involving very large deformations. We then revisit buckling instabilities in a finite, rectangular domain considered in previous papers. Embedded within this domain, parallel to the longer dimension we consider a stiff, layered beam under compression. We analyse folding up to 40% shortening. In the case of viscoelasticity we observe significant mode coupling in the nonlinear range, a second dominant wavelength emerges around 30- 40%axial shortening in a rather spectacular way. We propose to consider size effects due to internal structure (the thickness of the individual layers) within the framework of a couple stress theory. Couple stress theories involve second order spatial derivatives of the velocities/displacements in the virtual work principle. To avoid C1continuity in the finite element formulation we introduce the spin of the cross sections of the individual layers as an independent variable and enforce equality to the spin of the unit normal vector to the layers (-the director of the layer system-) by means of a penalty method. We illustrate the convergence of the penalty method by means of numerical solutions of simple shears of an infinite layer for increasing values of the penalty parameter. For the shear problem we present solutions assuming that the internal layering is oriented orthogonal to the surfaces of the shear layer initially. For high values of the ratio of the normal–to the shear viscosity the deformation concentrates in thin bands around to the layer surfaces. Also in the context of simple shear we associate different initial director (=normal vector to the internal layer planes) orientations to each particle of our particle advection finite element scheme. The initial distribution of director orientations is random. We then demonstrate the emergence of a schistose rock-like material in the course of finite simple shearing.
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hal-01007947 , version 1 (23-10-2018)


  • HAL Id : hal-01007947 , version 1


H. B. Muhlhaus, Frédéric Dufour, L. Moresi, B. Hobbs, H. Sakaguchi. Buckling and flow alignment in foliated rock. Exploration Geodynamics Chapman Conference, 2001, Dunsborough, Australia. ⟨hal-01007947⟩
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