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. doi:10.1111/j.1365-246X.2005.02742.x

Attached Files (Some files may be inaccessible until you login with your UQ eSpace credentials)
Name Description MIMEType Size Downloads
UQ9040_OA.pdf HBM-KRL-GJI-2005.pdf application/pdf 1.34MB 252

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
Publication date 2005-11
Sub-type Article (original research)
DOI 10.1111/j.1365-246X.2005.02742.x
Open Access Status File (Publisher version)
Volume 163
Issue 2
Start page 788
End page 800
Total pages 13
Place of publication Oxford, United Kingdom
Publisher Oxford University Press
Collection year 2005
Language eng
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
Mantle convection
Non-Newtonian rheology
Jaumann stress rates
Finite elements
Temperature dependent viscosity
Deborah Number
Geochemistry & Geophysics
Dependent Viscosity
References References Bercovici, D., A simple model of plate generation from mantle flow, Geophysical Journal International, 114, 635-650, 1993. Biot, M., The Mechanics of Incremental Deformations, John Wiley, New York, 1965. Braun, J., 3-Dimensional Numerical Simulations of Crustal-Scale Wrenching Using a Nonlinear Failure Criterion, Journal of Structural Geology, 16 (8), 1173-1186, 1994. Funiciello, F., G. Morra, K. Regenauer-Lieb, and D. Giardini, Dynamics of retreating slabs: 1. Insights from two-dimensional numerical experiments, Journal of Geophysical Research-Solid Earth, 108 (B4), art. no.-2206, 2003. Gurnis, M., C. Eloy, and S.J. Zhong, Free-surface formulation of mantle convection .2. Implication for subduction-zone observables, Geophysical Journal International, 127 (3), 719-727, 1996. Harder, H., Numerical-Simulation of Thermal-Convection with Maxwellian Viscoelasticity, Journal of Non-Newtonian Fluid Mechanics, 39 (1), 67-88, 1991. Hill, R, The Mathematical Theory of Plasticity, Oxford University Press, 1998 Kolymbas, D., and I. Herle, Shear and objective stress rates in hypoplasticity, International Journal for Numerical and Analytical Methods in Geomechanics, 27 (9), 733-744, 2003. Malvern,L. E., Introduction to the Mechanics of a Continuous Medium, Prentice-Hall, NJ., 1969. Miller, M., Lister G.S. and Kennett B., 2004. Three-dimensional structure of the Northwest Pacific margin. In: McPhie, J. and McGoldrick, P. (editors), Dynamic Earth; past, present and future, Geological Society of Australia, Abstracts. 73, 217. Melosh, H.J., Dynamic support of the outer rise, Geophysical Research Letters, 5, 321-324, 1978. Moresi, L., F. Dufour, and H. Muhlhaus, Mantle convection models with viscoelastic/brittle lithosphere: Numerical methodology and plate tectonic modeling, Pageoph, 159 (10), 2335, 2002. Moresi, L., and V. Solomatov, Mantle convection with a brittle lithosphere: thoughts on the global tectonic styles of the Earth and Venus, Geophysical Journal International, 133 (3), 669-682, 1998. Morra, G., K. Regenauer-Lieb, and D. Giardini, On the curvature of oceanic arcs, Nature, (submitted), 2004. Muhlhaus, H.B., and E.C. Aifantis, The Influence of Microstructure-Induced Gradients on the Localization of Deformation in Viscoplastic Materials, Acta Mechanica, 89 (1-4), 217-231, 1991. Muhlhaus, HB, Surface instability of a half space with bending stiffness (in German), Ing. Archive, 56, 383-388, 1985. Needleman, A., Material Rate Dependence and Mesh Sensitivity in Localization Problems. Comput. Methods Appl. Mech. Engrg., Vol. 67, pp. 69-85, 1988. Ogawa, M., Plate-like regime of a numerically modeled thermal convection in a fluid with temperature-, pressure-, and stress-history-dependent viscosity, Journal of Geophysical Research-Solid Earth, 108 (B2), 2003. Phan-Thien, N. Understanding viscoelasticity-basics of rheology, Springer Verlag, Berlin Heidelberg New York (2002) Parmentier, E.M., Turcotte, D.L. and Torrance, K.E. Studies of finite amplitude non-Newtonian thermal convection with application to convection in the Earth mantle. J. Geophys. Res., 81,1839-1846, (1976) Prager, William. Introduction to Mechanics of Continua. Boston, MA: Ginn, 1961. Poliakov, A., Y. Podladchikov, E. Dawson, and C.J. Talbot, Salt diapirism with simultaneous brittle faulting and viscous flow, Geological Society, 100, 291, 1996. Regenauer-Lieb, K., B. Hobbs, H. Mulhaus, A. Ord, D.A. Yuen, and S. van der Lee, Lithosphere fault zones rejuvenated, Tectonophysics, (submitted), 2004. Regenauer-Lieb, K., D. Yuen, and J. Branlund, The Initation of Subduction: Criticality by Addition of water?, Science, 294, 578-580, 2001. Regenauer-Lieb, K., and D.A. Yuen, Positive feedback of interacting ductile faults from coupling of equation of state, rheology and thermal-mechanics, Physics of Earth and Planetary Interiors, 142 (1-2), 113-135, 2004. Schmalholz, S.M. and Podladchikov, Y., Buckling versus folding: Importance of viscoelasticity. Geophysical Research Letters, 26(17): 2641-2644, 1999. Scholz, C.H. The mechanics of earthquakes and faulting, Cambridge University Press. 1990. Solomatov, V. Scaling of temperature-dependent and stress-dependent viscosity convection. Physics of Fluids 7(2), 266-274.1995 Stein, C.A., J. Schmalzl, and U. Hansen, The effect of rheological parameters on plate behaviour in a self-consitent model of mantle convection, Physics of the Earth and Planetary Interiors, in press, 2004. Tackley, P., Self-consistent generation of tectonic plates in three-dimensional mantle convection, Earth and Planetary Science Letters, 157, 9-22, 1998. Tackley, P., Self-consistent generation of tectonic plates in time- dependent, three-dimensional mantle convection simulations, 1. Pseudoplastic yielding, G3, 01 (23), 1525, 2000a. Tackley, P., Self-consistent generation of tectonic plates in time- dependent, three-dimensional mantle convection simulations. 2. Strain weakening and asthenosphere, G3, 01 (25), 2027, 2000b. Turcotte, D.L., How does Venus lose heat?, Journal of Geophysical Research, 100 (E8), 16931-16940, 1995. Turcotte, D.L. and Schubert, G, Geodynamics, 2nd edition, Cambridge University Press, 2002. Trompert,R. and Hansen, U. ,Mantle convection simulations with rheologies that generate plate-like behavior, Nature, 395, 686-689, 1998. Zienkiewicz, O.C. and Taylor, R.L., The Finite Element Method, Vol.3, 5th Edition, Butterworth/Heinemann, ISBN 0 7506 5050 8, 2000.
Q-Index Code C1
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

Version Filter Type
Citation counts: TR Web of Science Citation Count  Cited 27 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 33 times in Scopus Article | Citations
Google Scholar Search Google Scholar
Created: Tue, 25 Oct 2005, 10:00:00 EST by Hans-Bernd Muhlhaus on behalf of Faculty Of Engineering, Architecture & Info Tech