Kinetics of buckling of a compressed film on a viscous substrate

Sridhar, Nigamanth; Srolovitz, David J.; Suo, Zhigang

doi:10.1063/1.1368180

Cited by 101 publications

(77 citation statements)

References 6 publications

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“…A similar result for the vertical stress exerted by a finite, viscous matrix on the layer boundary was recently presented by Sridhar et al [2001] but for free slip conditions (t xz = 0 at layer-matrix boundary). Sridhar et al [2001] investigated buckling of an elastic layer resting on a finite, viscous matrix without the effects of gravity. Equations (30) and (31) are substituted into (1), and the resulting nondimensional amplification rate for folding of a ductile layer resting on a finite, viscous matrix under the effects of gravity is…”

Section: Folding Of a Ductile Layer Resting On Ansupporting

confidence: 48%

“…Results obtained with our analytical theory compare well with analytical and analogue results obtained by Ramberg [1963] for folding, while the matrix above and below the layer has the same finite thickness and gravity can be ignored. Sridhar et al [2001] showed that for folding of an elastic layer resting on a finite, viscous matrix, both the dominant wavelength and the maximal amplification rate decrease with decreasing matrix thickness. Therefore the matrix thickness has the same influence on the dominant wavelength and the maximal amplification rate, independent of layer rheology for both free slip and no slip between layer and matrix.…”

Section: Folding Of a Ductile Layer Resting On Anmentioning

confidence: 99%

“…[17] Note that all considered stress expressions for the viscous matrix (compare equations (9), (30), (38) and the one given by Sridhar et al [2001]) exhibit the same relation between stress, matrix viscosity, perturbation wavelength, and layer deflection and that additional multipliers (such as F det and F dd ) contain information on matrix thickness, viscosity variation, and boundary conditions at the layer-matrix boundary. The four stress expressions can be variously combined into (1) to simulate a number of different folding situations.…”

Section: Folding Of a Ductile Layer Resting On A Matrixmentioning

confidence: 99%

“…Whatever the scale, an important result of these analytical studies is a maximum of amplification rate for a certain fold wavelength, which is designated the dominant wavelength [Biot, 1961]. Dominant wavelengths of small-scale folds were investigated for elastic [e.g., Biot, 1961], elastoplastic [e.g., Johnson, 1980], viscous [e.g., Biot, 1961], ductile (non-Newtonian, power law) [e.g., Fletcher, 1974], and viscoelastic [e.g., Schmalholz andPodladchikov, 1999, 2001a] layers embedded in an infinitely thick (half-space) matrix and for elastic layers resting on a viscoelastic matrix [e.g., Hunt et al, 1996], elastic layers resting on a finite, viscous matrix [Sridhar et al, 2001], and viscous layers embedded in a finite, viscous matrix [Ramberg, 1963]. Dominant wavelengths of large-scale folds were expressed for elastic [Ramberg and Stephansson, 1964;Turcotte and Schubert, 1982] and ductile [Burov and Molnar, 1998;Cloetingh et al, 1999] layers.…”

Section: Introductionmentioning

confidence: 99%

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Control of folding by gravity and matrix thickness: Implications for large‐scale folding

2002

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[1] We show that folding of a non-Newtonian layer resting on a homogeneous Newtonian matrix with finite thickness under influence of gravity can occur by three modes: (1) matrix-controlled folding, dependent on the effective viscosity contrast between layer and matrix, (2) gravitycontrolled folding, dependent on the Argand number (the ratio of the stress caused by gravity to the stress caused by shortening), and (3) detachment folding, dependent on the ratio of matrix thickness to layer thickness. We construct a phase diagram that defines the transitions between each of the three folding modes. Our priority is transparency of the analytical derivations (e.g., thin-plate versus thick-plate approximations), which permits complete classification of the folding modes involving a minimum number of dimensionless parameters. Accuracy and sensitivity of the analytical results to model assumptions are investigated. In particular, depth dependence of matrix rheology is only important for folding over a narrow range of material parameters. In contrast, strong depth dependence of the viscosity of the folding layer limits applicability of ductile rheology and leads to a viscoelastic transition. Our theory is applied to estimate the effective thickness of the folded central Asian upper crust using the ratio of topographic wavelength to Moho depth. Phase diagrams based on geometrical parameters show that gravity does not significantly control folding in the Jura and the Zagros Mountains but does control folding in central Asia. Applicability conditions of viscous and thin sheet models for large-scale lithospheric deformation, derived in terms of the Argand number, have implications for the plate-like style of planetary tectonics.

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Section: Folding Of a Ductile Layer Resting On Ansupporting

confidence: 48%

Section: Folding Of a Ductile Layer Resting On Anmentioning

confidence: 99%

Section: Folding Of a Ductile Layer Resting On A Matrixmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Control of folding by gravity and matrix thickness: Implications for large‐scale folding

2002

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“…To describe the salient features of the wrinkle dynamics, here we give a simplified analysis, assuming that the BPSG layer is so thick that its thickness does not enter into the consideration. The analysis follows those in [28,40]. More comprehensive analyses are given in [29,-~31].…”

Section: Growing Wrinklesmentioning

confidence: 98%

Mechanics of relaxing SiGe islands on a viscous glass

et al. 2002

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A process has been developed recently to fabricate a structure comprising, from top to bottom, a SiGe thin film, a glass layer, and a Si wafer. The SiGe film is a perfect crystal, and is under biaxial compression. The SiGe film is patterned into islands. On annealing, the glass flows and the islands relax. The resulting strain-free islands are used as substrates, to grow epitaxial optoelectronic devices. This article describes a series of studies on the anneMing process, combining experiment and theory. A small island relaxes by expansion, starting at the edges and diffusing to the center. A large island wrinkles before the expansion reaches the center. After some time, the wrinkles either disappear, or cause the island to fracture. We model the island as an elastic plate, and the glass layer as a viscous liquid. The strains in the islands are measured by X-ray diffraction and Raman spectroscopy, and the wrinkle amplitudes by atomic force microscope. The data are compared with the theoretical predictions. We determine the conditions under which the islands relax by expansion without significant wrinkling, and demonstrate that a cap layer suppresses wrinkles, relaxing a large island crack-free.

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Spontaneous Formation of Ordered Lateral Patterns in Polymer Thin‐Film Structures

Okayasu

Zhang

Bucknall³

et al. 2004

Adv Funct Materials

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The understanding of the lateral morphology stability of thin polymer devices is of fundamental importance. In this work, the lateral morphology in a model system consisting of thin polymer films capped with thin metal layers on a Si substrate is investigated. When the model system is heated above a critical temperature, a characteristic surface topographic structure is observed that has a well‐defined periodicity but random orientation. It is shown that the minimum temperature, Tmin, required for the surface pattern to be observed decreases with increasing polymer‐film thickness. Increasing either the metal‐ or polymer‐layer thickness increases the characteristic wavelength of the topography. It is believed that the dominating driving force for the surface corrugated‐pattern formation is the thermal‐expansion‐coefficient mismatch of the capping layer and the substrate. A theoretical model based on local bending of a thin, stiff surface film on a thin, elastic medium is used to provide a quantitative analysis of the surface morphology. The calculated minimum temperature required for the surface morphology and the periodicity of the surface patterns to form are in strong agreement with the experimental results. By contrast, systems with prefabricated topographic patterns within any of the three layers (polymer, metal, substrate) produce highly anisotropic surface topographies aligned perpendicular to the prefabricated topographic structure. It is also found that, in a model system with pre‐patterned polymer films, a much higher critical temperature is required for the surface morphology to be observed. The changes in apparent stability and morphological orientation in the pre‐patterned systems can be understood as a result of the anisotropic release of the lateral surface stress during the heat treatment.

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Kinetics of buckling of a compressed film on a viscous substrate

Cited by 101 publications

References 6 publications

Control of folding by gravity and matrix thickness: Implications for large‐scale folding

Control of folding by gravity and matrix thickness: Implications for large‐scale folding

Mechanics of relaxing SiGe islands on a viscous glass

Spontaneous Formation of Ordered Lateral Patterns in Polymer Thin‐Film Structures

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