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            <title xml:lang="en">Buckling and flow alignment in foliated rock</title>
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                <forename type="first">H. B.</forename>
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                <forename type="first">Frédéric</forename>
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                <forename type="first">H.</forename>
                <surname>Sakaguchi</surname>
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            <idno type="halRefHtml">&lt;i&gt;Exploration Geodynamics Chapman Conference&lt;/i&gt;, 2001, Dunsborough, Australia</idno>
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                <title xml:lang="en">Buckling and flow alignment in foliated rock</title>
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                    <forename type="first">H. B.</forename>
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                    <forename type="first">Frédéric</forename>
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              <p>A model for finely layered visco-elastic rock proposed by us in previous papers is used as the basic unitfor a granular rock. The grains are distinguished by individual layer orientations. Initially the layerorientations are randomly distributed. Size effects are considered within the framework of a couplestress theory. We begin with an outline of the governing equations for the standard continuum case andapply a computational simulation scheme suitable for problems involving very large deformations. Wethen 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 undercompression. We analyse folding up to 40% shortening. In the case of viscoelasticity we observesignificant 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 internalstructure (the thickness of the individual layers) within the framework of a couple stress theory. Couplestress theories involve second order spatial derivatives of the velocities/displacements in the virtualwork principle. To avoid C1continuity in the finite element formulation we introduce the spin of the crosssections of the individual layers as an independent variable and enforce equality to the spin of the unitnormal vector to the layers (-the director of the layer system-) by means of a penalty method. Weillustrate the convergence of the penalty method by means of numerical solutions of simple shears of aninfinite layer for increasing values of the penalty parameter. For the shear problem we present solutionsassuming that the internal layering is oriented orthogonal to the surfaces of the shear layer initially. Forhigh values of the ratio of the normal–to the shear viscosity the deformation concentrates in thin bandsaround 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 finiteelement scheme. The initial distribution of director orientations is random. We then demonstrate theemergence of a schistose rock-like material in the course of finite simple shearing.</p>
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