A two‐phase composite in simple shear: Effective mechanical anisotropy development and localization potential

Dąbrowski, Marcin; Schmid, Daniel W.; Podladchikov, Y. Y.

doi:10.1029/2012jb009183

Cited by 36 publications

(50 citation statements)

References 45 publications

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“…Dashed lines indicate the theoretical upper and lower bound given in and . Solid colored lines denote the aDEM approximation by Dabrowski et al () and the SCA approximations by Fletcher () and Treagus (). Gray areas indicate where numerical results become less reliable due to loss of resolution.…”

Section: Resultsmentioning

confidence: 99%

“…The change of aspect ratio

r

and orientation

θ

of an elliptical inclusion is given by

\overset{r}{true} = 2 r {\overset{ε}{true}}_{x x}^{i n c l}

\overset{θ}{true} = W_{x y}^{i n c l} + \frac{r^{2} + 1}{r^{2} - 1} {\overset{ε}{true}}_{x y}^{i n c l}

where

{\overset{ε}{true}}_{x x}^{i n c l}

{\overset{ε}{true}}_{x y}^{i n c l}

and

W_{x y}^{i n c l}

are deformation and vorticity inside the inclusion. These can be related to the far field deformation rates and vorticity as follows (Dabrowski et al, ; Fletcher, ):

{\overset{ε}{true}}_{x x}^{i n c l} = \frac{\sqrt{\frac{β_{n}}{β_{s}}} + p}{normalΔ η_{n} \sqrt{\frac{β_{n}}{β_{s}}} + p} {\overset{ε}{true}}_{x x}^{\infty}

{\overset{ε}{true}}_{x y}^{i n c l} = \frac{\sqrt{\frac{β_{n}}{β_{s}}} + p}{\sqrt{β_{}}}

…”

Section: Methodsmentioning

confidence: 99%

“…Comparing the analytical prediction to the results from numerical models, Dabrowski et al () showed that the analytical solution does predict the evolution of a two‐phase medium with initially spherical inclusions up to a shear strain of

γ = 1

. At larger strains, predictions and model results start to diverge, the main reason being the interaction between different inclusions which result in nonelliptical inclusion shapes.…”

Section: Methodsmentioning

confidence: 99%

“…The issue of strain localization due to weak phase alignment is not only of importance in the lower mantle but even more so in the lithosphere, where it may result in large‐scale shear zones that ultimately enable subduction initiation (e.g., Montési, ). For this reason, past numerical studies of such systems have attempted to develop a parameterization of the impact of weak phase topology on the effective rheology for specific inclusion shapes such as layers, squares, or ellipses (e.g., Dabrowski et al, ; Fletcher, ; Handy, , ; Takeda, ; Takeda & Griera, ; Treagus, ; Tullis et al, ). More recently, both Cook et al () and Gerbi et al () also considered the effect of more complex morphologies on the effective rheology of power law materials.…”

Section: Introductionmentioning

confidence: 99%

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Ferropericlase Control of Lower Mantle Rheology: Impact of Phase Morphology

Thielmann

Golabek

Marquardt

2020

Geochem Geophys Geosyst

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The rheological properties of Earth's lower mantle play a key role for global mantle dynamics. The mineralogy of the lower mantle can be approximated as a bridgmanite‐ferropericlase mixture. Previous work has suggested that the deformation of this mixture might be dramatically affected by the large differences in viscosity between bridgmanite and ferropericlase. Here, we employ numerical models to establish a connection between ferropericlase morphology and the effective rheology of the Earth's lower mantle using a numerical‐statistical approach. Using this approach, we link the statistical properties of the two‐phase composite to its effective viscosity tensor using analytical approximations. We find that ferropericlase develops elongated structures within the bridgmanite matrix that result in significantly lowered viscosity. While our findings confirm previous endmember models that suggested a change of mantle viscosity due to the formation of interconnected weak layers, we show that significant rheological weakening can thus be already achieved even when ferropericlase does not form an interconnected network. Additionally, the alignment of weak ferropericlase leads to a pronounced viscous anisotropy that develops with total strain, which may have implications for understanding the viscosity structure of Earth's lower mantle as well as for modeling the behavior of subducting slabs. We show that to capture the effect of ferropericlase elongation on the effective viscosity tensor (and its anisotropy) in large‐scale mantle convection models, the analytical approximations that have been derived to describe the evolution of the effective viscosity of a two‐phase medium with aligned elliptical inclusions can be used.

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Section: Resultsmentioning

confidence: 99%

“…The change of aspect ratio

r

and orientation

θ

of an elliptical inclusion is given by

\overset{r}{true} = 2 r {\overset{ε}{true}}_{x x}^{i n c l}

\overset{θ}{true} = W_{x y}^{i n c l} + \frac{r^{2} + 1}{r^{2} - 1} {\overset{ε}{true}}_{x y}^{i n c l}

where

{\overset{ε}{true}}_{x x}^{i n c l}

{\overset{ε}{true}}_{x y}^{i n c l}

and

W_{x y}^{i n c l}

are deformation and vorticity inside the inclusion. These can be related to the far field deformation rates and vorticity as follows (Dabrowski et al, ; Fletcher, ):

{\overset{ε}{true}}_{x x}^{i n c l} = \frac{\sqrt{\frac{β_{n}}{β_{s}}} + p}{normalΔ η_{n} \sqrt{\frac{β_{n}}{β_{s}}} + p} {\overset{ε}{true}}_{x x}^{\infty}

{\overset{ε}{true}}_{x y}^{i n c l} = \frac{\sqrt{\frac{β_{n}}{β_{s}}} + p}{\sqrt{β_{}}}

…”

Section: Methodsmentioning

confidence: 99%

γ = 1

. At larger strains, predictions and model results start to diverge, the main reason being the interaction between different inclusions which result in nonelliptical inclusion shapes.…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Ferropericlase Control of Lower Mantle Rheology: Impact of Phase Morphology

Thielmann

Golabek

Marquardt

2020

Geochem Geophys Geosyst

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“…14). Theoretical analyses have proved the development of shear bands as a consequence of inhomogeneities in the deforming material (Dabrowski et al, 2012). The preferred mechanisms involved in shear localization are (i) grain-size reduction (Braun et al, 1999); (ii) thermal effect induced by shear heating (Kaus and Podladchikov, 2006) or magmatic intrusions (Tommasi et al, 1994); (iii) crystal shape or orientation (Bystricky et al, 2000;Takeda and Griera, 2006); and (iv) presence of fluid (Fusseis et al, 2009).…”

Section: Shear Zonesmentioning

confidence: 99%

Textures and melt-crystal-gas interactions in granites

Vigneresse¹

2015

Geoscience Frontiers

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a b s t r a c tFelsic intrusions present ubiquitous structures. They result from the differential interactions between the magma components (crystal, melt, gas phase) while it flows or when the flow is perturbed by a new magma injection. The most obvious structure consists in fabrics caused by the interactions of rotating grains in a flowing viscous melt. New magma inputs through dikes affect the buk massif flow, considered as global within each mineral facies. A review of the deformation and flow types developing in a magma chamber identifis the patterns that could be expected. It determines their controlling parameters and summarizes the tools for their quantification. Similarly, a brief review of the rheology of a complex multiphase magma identifies and suggests interactions between the different components. The specific responses each component presents lead to instability development. In particular, the change in vorticity orientation, associated with the switch between monoclinic to triclinic flow is a cause of many instabilities. Those are preferentially local. Illustrations include fabric development, shear zones and flow banding. They depend of the underlying rheology of interacting magmas. Dikes, enclaves, schlieren and ladder dikes result from the interactions between the magma components and changing boundary conditions. Orbicules, pegmatites, unidirectional solidification textures and miarolitic cavities result from the interaction of the melt with a gaseous phase. The illustrations examine what is relevant to the bulk flow, local structures or boundary conditions. In each case a field observation illustrates the instability. The discussion reformulates instability observations, suggesting new trails for ther description and interpretation in terms of local departure to a bulk flow. A brief look at larger structures and at their evolution tries to relate these instabilities on a broader scale. The helical structures of the Rí cany pluton, Czech Republic and by the multiple granitic intrusions of Dolbel, Niger illustrate such events.Ó 2014, China University of Geosciences (Beijing) and Peking University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

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The Minimized Power Geometric model: An analytical mixing model for calculating polyphase rock viscosities consistent with experimental data

2014

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Here we introduce the Minimized Power Geometric (MPG) model which predicts the viscosity of any polyphase rocks deformed during ductile flow. The volumetric fractions and power law parameters of the constituting phases are the only model inputs required. The model is based on a minimization of the mechanical power dissipated in the rock during deformation. In contrast to existing mixing models based on minimization, we use the Lagrange multipliers method and constraints of strain rate and stress geometric averaging. This allows us to determine analytical expressions for the polyphase rock viscosity, its power law parameters, and the partitioning of strain rate and stress between the phases. The power law bulk behavior is a consequence of our model and not an assumption. Comparison of model results with 15 published experimental data sets on two-phase aggregates shows that the MPG model reproduces accurately both experimental viscosities and creep parameters, even where large viscosity contrasts are present. In detail, the ratio between experimental and MPG-predicted viscosities averages 1.6. Deviations from the experimental values are likely to be due to microstructural processes (strain localization and coeval other deformation mechanisms) that are neglected by the model. Existing models that are not based on geometric averaging show a poorer fit with the experimental data. As long as the limitations of the mixing models are kept in mind, the MPG model offers great potential for applications in structural geology and numerical modeling.

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A two‐phase composite in simple shear: Effective mechanical anisotropy development and localization potential

Cited by 36 publications

References 45 publications

Ferropericlase Control of Lower Mantle Rheology: Impact of Phase Morphology

Ferropericlase Control of Lower Mantle Rheology: Impact of Phase Morphology

Textures and melt-crystal-gas interactions in granites

The Minimized Power Geometric model: An analytical mixing model for calculating polyphase rock viscosities consistent with experimental data

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