A director theory for visco-elastic folding instabilities in multilayered rock

Muhlhaus, HB, Dufour, F, Moresi, L and Hobbs, B (2002) A director theory for visco-elastic folding instabilities in multilayered rock. International Journal of Solids And Structures, 39 13-14: 3675-3691.


Author Muhlhaus, HB
Dufour, F
Moresi, L
Hobbs, B
Title A director theory for visco-elastic folding instabilities in multilayered rock
Journal name International Journal of Solids And Structures   Check publisher's open access policy
Publication date 2002
Sub-type Article
DOI 10.1016/S0020-7683(02)00175-0
Volume number 39
Issue number 13-14
ISSN 0020-7683
Start page 3675
End page 3691
Total pages 17
Place of publication Oxford
Publisher Pergamon-elsevier Science Ltd
Language eng
Abstract A model for finely layered visco-elastic rock proposed by us in previous papers is revisited and generalized to include couple stresses. 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 consider buckling instabilities in a finite, rectangular domain. Embedded within this domain, parallel to the longer dimension we consider a stiff, layered beam under compression. We analyse folding up to 40% shortening. The standard continuum solution becomes unstable for extreme values of the shear/normal viscosity ratio. The instability is a consequence of the neglect of the bending stiffness/viscosity in the standard continuum model. We suggest considering these effects 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 C-1 continuity 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. The effect of couple stresses on the evolution of folds in layered structures is also investigated. (C) 2002 Elsevier Science Ltd. All rights reserved.
Keyword Mechanics
Deformation
Lithosphere
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

 
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Created: Mon, 13 Aug 2007, 13:03:04 EST