egu vienna 04/17/2007 m. frehner & s.m. schmalholz 1 numerical simulations of parasitic folding...
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![Page 1: EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz 1 Numerical simulations of parasitic folding and strain distribution in multilayers EGU Vienna, April](https://reader035.vdocument.in/reader035/viewer/2022081603/56649d8e5503460f94a76fe7/html5/thumbnails/1.jpg)
1EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz
Numerical simulations of parasitic foldingand strain distribution in multilayers
EGU Vienna, April 17, 2007
Marcel FrehnerStefan M. Schmalholz
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2EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz
Motivation: Asymmetric parasitic folds on all scales
Mount RubinWestern Antarctica
Picture courtesyof Chris Wilson
~1200m
Foliated MetagabbroVal Malenco; Swiss Alps
Picture courtesy of Jean-Pierre Burg
| Methods | Two-layer folds | Multilayer folds | Conclusions | Outlook || Motivation
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3EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz
Motivation: The work by Hans Ramberg
Ramberg, 1963: Evolution of drag foldsGeological Magazine
| Methods | Two-layer folds | Multilayer folds | Conclusions | Outlook || Motivation
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
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4EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz
Methods: Numerics
Self-developed 2D finite element (FEM) program
Incompressible Newtonianrheology
Mixed v-p-formulation
Half wavelengthof large folds
Viscosity contrast: 100
| Two-layer folds | Multilayer folds | Conclusions | Outlook || Motivation | Methods
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5EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz
Methods: Standard visualization
Resolution 11’250
elements
100’576 nodes
| Two-layer folds | Multilayer folds | Conclusions | Outlook || Motivation | Methods
Layer-parallel strainrate
40% shortening
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6EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz
Strain ellipse: A reminder
| Two-layer folds | Multilayer folds | Conclusions | Outlook || Motivation | Methods
1
1
x x
y y
t
u u
x yx x
u uy y
x y
G
Haupt, 2002:Continuum Mechanics and Theory of Materials
Ramsay and Huber, 1983:Strain Analysis
TC F F
Incremental deformationgradient tensor G
Finite deformationgradient tensor F
Right Cauchy-Green tensor C
Eigenvalues and eigenvectors are usedto calculate principal strain axes
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7EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz
Two-layer folds: Strain distribution
Color:Accumulated strain Color: Rotation angle
| Methods | Multilayer folds | Conclusions | Outlook || Motivation | Two-layer folds
40% shortenig
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8EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz
Two-layer folds: Three phases of deformation
Fold limb S Transition zone JFold hinge I
| Methods | Multilayer folds | Conclusions | Outlook || Motivation | Two-layer folds
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9EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz
Two-layer folds: Results of strain analysis
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
SI J
| Methods | Multilayer folds | Conclusions | Outlook || Motivation | Two-layer folds
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10EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz
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
| Methods | Two-layer folds | Conclusions | Outlook || Motivation | Multilayer folds
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11EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz
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
| Methods | Two-layer folds | Conclusions | Outlook || Motivation | Multilayer folds
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12EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz
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
| Methods | Two-layer folds | Conclusions | Outlook || Motivation | Multilayer folds
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13EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz
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
| Methods | Two-layer folds | Multilayer folds | Outlook || Motivation | Conclusions
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14EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz
Acc
um
ula
ted
stra
in
Acc
um
ula
ted
stra
in
Layer n=5, Matrix n=5
| Methods | Two-layer folds | Multilayer folds | Conclusions| Motivation || Outlook
Layer n=1, Matrix n=1
Work in progress: More complex rheology
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15EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz
Work in progress: More complex geometry
| Methods | Two-layer folds | Multilayer folds | Conclusions| Motivation || Outlook
Different thicknesses
Random initial perturbation on all layers
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16EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz
Thank you
Frehner, M. and Schmalholz S.M., 2006:Numerical simulations of parasitic folding in multilayersJournal of Structural Geology