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Numerical simulations of parasitic folding and strain distribution in multilayers

This study presents numerical simulations of parasitic folding in multilayers, aiming to test and quantify the strain field and visualize the deformation. The results verify Ramberg's hypothesis and reveal three phases of deformation in a two-layer system. The presence of thin multilayers has little effect on the deformation of the two-layer system. Further work is in progress to incorporate more complex rheology and geometry.

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Numerical simulations of parasitic folding and strain distribution in multilayers

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  1. Numerical simulations of parasitic foldingand strain distribution in multilayers EGU Vienna, April 17, 2007 Marcel FrehnerStefan M. Schmalholz frehner@erdw.ethz.ch

  2. ~1200m Mount RubinWestern Antarctica Picture courtesyof Chris Wilson Foliated MetagabbroVal Malenco; Swiss Alps Picture courtesy of Jean-Pierre Burg |Methods | Two-layer folds | Multilayer folds | Conclusions | Outlook | | Motivation Motivation: Asymmetric parasitic folds on all scales

  3. |Methods | Two-layer folds | Multilayer folds | Conclusions | Outlook | | Motivation Motivation: The work by Hans Ramberg • Ramberg‘s hypothesis for parasitic folding • Thin layers buckle first • Asymmetry by shearing between the larger folds • Aim • Test hypothesis with numerical methods • Quantify and visualize strain field Ramberg, 1963: Evolution of drag foldsGeological Magazine

  4. |Two-layer folds | Multilayer folds | Conclusions | Outlook | | Motivation | Methods Methods: Numerics • Self-developed 2D finite element (FEM) program • Incompressible Newtonianrheology • Mixed v-p-formulation • Half wavelengthof large folds • Viscosity contrast: 100

  5. 40% shortening Layer-parallel strainrate |Two-layer folds | Multilayer folds | Conclusions | Outlook | | Motivation | Methods Methods: Standard visualization • Resolution • 11’250 elements • 100’576 nodes

  6. |Two-layer folds | Multilayer folds | Conclusions | Outlook | | Motivation | Methods Strain ellipse: A reminder • Incremental deformationgradient tensor G • Finite deformationgradient tensor F • Right Cauchy-Green tensor C • Eigenvalues and eigenvectors are usedto calculate principal strain axes Haupt, 2002:Continuum Mechanics and Theory of Materials Ramsay and Huber, 1983:Strain Analysis

  7. | Methods |Multilayer folds | Conclusions | Outlook | | Motivation | Two-layer folds Two-layer folds: Strain distribution 40% shortenig Color:Accumulated strain Color: Rotation angle

  8. | Methods |Multilayer folds | Conclusions | Outlook | | Motivation | Two-layer folds Two-layer folds: Three phases of deformation Fold limb S Transition zone JFold hinge I

  9. | Methods |Multilayer folds | Conclusions | Outlook | | Motivation | Two-layer folds Two-layer folds: Results of strain analysis I • Three regions of deformation • Fold hinge, layer-parallel compression only • Fold limb • Transition zone, complicated deformation mechanism • Three deformation phases at fold limb • Layer-parallel compression • Shearing without flattening • Flattening normal to the layers J S

  10. | Methods | Two-layer folds |Conclusions | Outlook | | Motivation | Multilayer folds Multilayer folds: Example of numerical simulation • Viscositycontrast: 100 • Thickness ratioHthin:Hthick = 1:50 • Random initial perturbation onthin layers • Truly multiscale model • Number of thin layers in this example: 20 • Resolution: • 24‘500 elements • 220‘500 nodes

  11. | Methods | Two-layer folds |Conclusions | Outlook | | Motivation | Multilayer folds Multilayer folds: Results • Layer-parallel compression • No buckling of thick layers • Buckling of thin layersSymmetric fold stacks • Shearing without flattening • Buckling of thick layers: shearing between them • Stacks of multilayer folds become asymmetric • Flattening normal to layers • Increased amplification of thick layers:flattening normal to layers • Amplitudes of thin layers decrease

  12. | Methods | Two-layer folds |Conclusions | Outlook | | Motivation | Multilayer folds Multilayer folds: Similarity to two-layer folding • Deformation of two-layersystem is nearly independentof presence of multilayerstack in between 50% shortening: Black: Multilayer systemGreen: Two-layer system

  13. | Methods | Two-layer folds | Multilayer folds |Outlook | | Motivation | Conclusions Conclusions • Efficient strain analysis with computed strain ellipses • Ramberg‘s hypothesis verified • 3 phases of deformation between a two-layer system • Layer parallel compression: Thin layers build vertical symmetric fold-stacks • Shearing without flattening: Asymmetry of thin layers • Flattening normal to layers: Decrease of amplitude of thin layers • Presence of thin multilayers hardly affectsdeformation of two-layer system

  14. Accumulated strain Layer n=5, Matrix n=5 | Methods | Two-layer folds | Multilayer folds | Conclusions | Outlook | Motivation | Work in progress: More complex rheology Accumulated strain Layer n=1, Matrix n=1

  15. | Methods | Two-layer folds | Multilayer folds | Conclusions | Outlook | Motivation | Work in progress: More complex geometry • Different thicknesses • Random initial perturbation on all layers

  16. Thank you Frehner, M. and Schmalholz S.M., 2006:Numerical simulations of parasitic folding in multilayersJournal of Structural Geology

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