Towards a Self Consistent Plate Mantle Model that Includes Elasticity: Simple Benchmarks and Application to Basic Modes of Convection

Muhlhaus, Hans-Bernd and Regenauer-Lieb, Klaus (2005) Towards a Self Consistent Plate Mantle Model that Includes Elasticity: Simple Benchmarks and Application to Basic Modes of Convection. Geophysical Journal International, 163 2: 788-800.

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Author Muhlhaus, Hans-Bernd
Regenauer-Lieb, Klaus
Title Towards a Self Consistent Plate Mantle Model that Includes Elasticity: Simple Benchmarks and Application to Basic Modes of Convection
Journal name Geophysical Journal International   Check publisher's open access policy
ISSN 0956-540X
0955-419X
1365-246X
Publication date 2005-11
Sub-type Article (original research)
DOI 10.1111/j.1365-246X.2005.02742.x
Volume 163
Issue 2
Start page 788
End page 800
Total pages 13
Place of publication Oxford
Publisher Blackwell Scientific Publications
Collection year 2005
Language eng
Subject 260108 Geotectonics
C1
260206 Earthquake Seismology
780104 Earth sciences
Abstract One of the difficulties with self consistent plate-mantle models capturing multiple physical features, such as elasticity, non-Newtonian flow properties, and temperature dependence, is that the individual behaviours cannot be considered in isolation. For instance, if a viscous mantle convection model is generalized naively to include hypo-elasticity, then problems based on Earth-like Rayleigh numbers exhibit almost insurmountable numerical stability issues due to spurious softening associated with the co-rotational stress terms. If a stress limiter is introduced in the form of a power law rheology or yield criterion these difficulties can be avoided. In this paper, a novel Eulerian finite element formulation for visco-elastic convection is presented and the implementation of the co-rotational stress terms is addressed. The salient dimensionless numbers of visco-elastic plastic flows such as Weissenberg, Deborah and Bingham numbers are discussed in a separate section in the context of Geodynamics. We present an Eulerian formulation for slow temperature dependent, visco-elastic-plastic flows. A consistent tangent (incremental) formulation of the governing equations is derived. Numerical and analytical solutions demonstrating the effect of visco-elasticity, co-rotational terms are first discussed for simplified benchmark problems. For flow around cylinders we identify parameter ranges of predominantly viscous and visco-plastic and transient behavior. The influence of locally high strain rates on the importance of elasticity and non-Newtonian effects is also discussed in this context. For the case of simple shear we investigate in detail the effect of different co-rotational stress rates and the effect of power law creep. The results show that the effect of the co-rotational terms is insignificant if realistic stress levels are considered (e.g. deviatoric invariant smaller than 1/10 of the shear modulus say). We also consider the basic convection modes of stagnant lid, episodic resurfacing and mobile lid convection as applicable to a cooling planet. The simulations show that elasticity does not have a significant effect on global parameters such as the Nusselt number and the qualitative nature of the basic convection pattern. Our simple benchmarks show, however, also that elasticity plays a significant role for instabilities on the local scale of an individual subduction zone.
Keyword periodicity
computational geodynamics
Subduction
mantle convection
non-Newtonian rheology
Jaumann stress rates
finite elements
temperature dependent viscosity
Visco-elasticity
Plasticity
Convection
Deborah Number
Co-rotational
Geochemistry & Geophysics
Thermal-convection
Dependent Viscosity
Stress
Lithosphere
Rheology
Shear
Viscoelasticity
Simulations
Generation
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Additional Notes Originally published as Muhlhaus, Hans-Bernd and Regenauer-Lieb, Klaus (2005) Towards a Self Consistent Plate Mantle Model that Includes Elasticity: Simple Benchmarks and Application to Basic Modes of Convection. Geophysical Journal International 163:788-800. doi:10.1111/j.1365-246X.2005.02742.x

 
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