### Abstract

Initiation of cylindrical structures by buckling or necking in an anisotropic power-law fluid is treated for general plane flow. The principal axis of anisotropy, x′, in the stiffest direction in shortening or extension may be viewed as the trace of a foliation or lamination. Plane-flow constitutive relations between components of rate of deformation, D′_{xx} and D′_{xy}, and of deviatoric stress, s′_{xx} and s′_{xy}, for the fluid are D′_{xx} = B(Y′_{2}^{[(n-1)/2]}s′_{xx} and D′_{xy} = a^{2} B(Y′_{2} ^{[(n-1)sol;2]}s′_{xy}, where Y′_{2} = (s′_{xx})^{2} + a^{2}(s′_{xy})^{2} is an anisotropic invariant, a^{2} is the anisotropy parameter, and n is the stress exponent. We determine the rate of amplification of wavelength components in the deflection of the foliation, θ, from a mean orientation parallel to x. Linearly independent, or non-interacting normal modes have a periodic, band-like form θ(x,y) ≅ ∂ζ/∂x = -(λ A) sin[λ (x - vy)], where ζ is the height of a foliation trace above its mean plane, v=tanβ, where β is the angle between the normal to mean foliation and the axial surface, positive clockwise, and L=2π/λ is the foliation-parallel wavelength. Evolution of a component may be followed through a finite bulk deformation provided θ remains ≪1. The growth rate of slope, λA, is independent of L. Components with axial plane normal to the foliation (β=0) are strongly amplified in foliation-parallel shortening. If n > > 1, internal necking (boudinage) occurs in foliation-parallel extension for components with axial plane inclined at a large angle to the foliation normal. In combined shortening and shear, the most rapidly growing component has an axial plane that dips steeply in the direction of shear. For n>1, maximum instability occurs for combined foliation-parallel shear and shortening rather than pure shortening. Weak instability is present in foliation-parallel shear. This anisotropic nonlinear fluid approximates the behavior of an isotropic power-law medium containing preferentially oriented but anastomosing slip surfaces, or that of a rock in which a stiffer component of lenticular form is embedded in a softer matrix.

Original language | English (US) |
---|---|

Pages (from-to) | 1155-1167 |

Number of pages | 13 |

Journal | Journal of Structural Geology |

Volume | 27 |

Issue number | 7 |

DOIs | |

State | Published - Jul 1 2005 |

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### All Science Journal Classification (ASJC) codes

- Geology

### Cite this

*Journal of Structural Geology*,

*27*(7), 1155-1167. https://doi.org/10.1016/j.jsg.2004.08.002

}

*Journal of Structural Geology*, vol. 27, no. 7, pp. 1155-1167. https://doi.org/10.1016/j.jsg.2004.08.002

**Instability of an anisotropic power-law fluid in a basic state of plane flow.** / Fletcher, Raymond Charles.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Instability of an anisotropic power-law fluid in a basic state of plane flow

AU - Fletcher, Raymond Charles

PY - 2005/7/1

Y1 - 2005/7/1

N2 - Initiation of cylindrical structures by buckling or necking in an anisotropic power-law fluid is treated for general plane flow. The principal axis of anisotropy, x′, in the stiffest direction in shortening or extension may be viewed as the trace of a foliation or lamination. Plane-flow constitutive relations between components of rate of deformation, D′xx and D′xy, and of deviatoric stress, s′xx and s′xy, for the fluid are D′xx = B(Y′2[(n-1)/2]s′xx and D′xy = a2 B(Y′2 [(n-1)sol;2]s′xy, where Y′2 = (s′xx)2 + a2(s′xy)2 is an anisotropic invariant, a2 is the anisotropy parameter, and n is the stress exponent. We determine the rate of amplification of wavelength components in the deflection of the foliation, θ, from a mean orientation parallel to x. Linearly independent, or non-interacting normal modes have a periodic, band-like form θ(x,y) ≅ ∂ζ/∂x = -(λ A) sin[λ (x - vy)], where ζ is the height of a foliation trace above its mean plane, v=tanβ, where β is the angle between the normal to mean foliation and the axial surface, positive clockwise, and L=2π/λ is the foliation-parallel wavelength. Evolution of a component may be followed through a finite bulk deformation provided θ remains ≪1. The growth rate of slope, λA, is independent of L. Components with axial plane normal to the foliation (β=0) are strongly amplified in foliation-parallel shortening. If n > > 1, internal necking (boudinage) occurs in foliation-parallel extension for components with axial plane inclined at a large angle to the foliation normal. In combined shortening and shear, the most rapidly growing component has an axial plane that dips steeply in the direction of shear. For n>1, maximum instability occurs for combined foliation-parallel shear and shortening rather than pure shortening. Weak instability is present in foliation-parallel shear. This anisotropic nonlinear fluid approximates the behavior of an isotropic power-law medium containing preferentially oriented but anastomosing slip surfaces, or that of a rock in which a stiffer component of lenticular form is embedded in a softer matrix.

AB - Initiation of cylindrical structures by buckling or necking in an anisotropic power-law fluid is treated for general plane flow. The principal axis of anisotropy, x′, in the stiffest direction in shortening or extension may be viewed as the trace of a foliation or lamination. Plane-flow constitutive relations between components of rate of deformation, D′xx and D′xy, and of deviatoric stress, s′xx and s′xy, for the fluid are D′xx = B(Y′2[(n-1)/2]s′xx and D′xy = a2 B(Y′2 [(n-1)sol;2]s′xy, where Y′2 = (s′xx)2 + a2(s′xy)2 is an anisotropic invariant, a2 is the anisotropy parameter, and n is the stress exponent. We determine the rate of amplification of wavelength components in the deflection of the foliation, θ, from a mean orientation parallel to x. Linearly independent, or non-interacting normal modes have a periodic, band-like form θ(x,y) ≅ ∂ζ/∂x = -(λ A) sin[λ (x - vy)], where ζ is the height of a foliation trace above its mean plane, v=tanβ, where β is the angle between the normal to mean foliation and the axial surface, positive clockwise, and L=2π/λ is the foliation-parallel wavelength. Evolution of a component may be followed through a finite bulk deformation provided θ remains ≪1. The growth rate of slope, λA, is independent of L. Components with axial plane normal to the foliation (β=0) are strongly amplified in foliation-parallel shortening. If n > > 1, internal necking (boudinage) occurs in foliation-parallel extension for components with axial plane inclined at a large angle to the foliation normal. In combined shortening and shear, the most rapidly growing component has an axial plane that dips steeply in the direction of shear. For n>1, maximum instability occurs for combined foliation-parallel shear and shortening rather than pure shortening. Weak instability is present in foliation-parallel shear. This anisotropic nonlinear fluid approximates the behavior of an isotropic power-law medium containing preferentially oriented but anastomosing slip surfaces, or that of a rock in which a stiffer component of lenticular form is embedded in a softer matrix.

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U2 - 10.1016/j.jsg.2004.08.002

DO - 10.1016/j.jsg.2004.08.002

M3 - Article

AN - SCOPUS:23944439639

VL - 27

SP - 1155

EP - 1167

JO - Journal of Structural Geology

JF - Journal of Structural Geology

SN - 0191-8141

IS - 7

ER -