Scaled amplification equation: A key to the folding history of buckled viscous single-layers |
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| Authors: | Stefan M Schmalholz |
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| Institution: | aGeological Institut, ETH Zurich, 8092 Zurich, Switzerland |
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| Abstract: | The presented equation describes amplitude growth during viscous single-layer folding (buckling) up to high amplitudes. The equation relates the dimensionless fold amplitude (i.e. ratio of amplitude to wavelength) to the stretch (ratio of initial wavelength to instantaneous wavelength) for given values of the viscosity contrast between layer and surrounding material and the initial ratio of amplitude to wavelength. The amplification equation is suitably scaled so that all amplitude versus stretch curves for different values of viscosity contrasts and initial amplitudes fall onto essentially a single curve. The scaled amplification equation allows for representing fold amplification of viscous single-layers by a singular curve. The scaling parameter is the crossover strain, which is an estimate for the amount of strain that is accumulated during the initial stages of folding where the amplitude grows exponentially with strain. The singular curve allows quantifying the universal boundaries between the three folding stages, namely nucleation, amplification and kinematic growth. The scaled amplification equation is verified by numerical (finite element method) simulations of folding of single layers with initial random perturbations of the layer interfaces. The amplification equation describes the amplification of single folds within fold trains successfully, although the folds are neither regular nor periodic and vary considerably in shape. The easily measurable parameters, vertical and horizontal hinge distance, are shown to be good approximations for the analytical parameters amplitude and wavelength, respectively. |
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| Keywords: | Single-layer folding Scaling Finite elements Analytical solution Viscous flow |
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