Towards a self-consistent plate mantle model that includes elasticity: Simple benchmarks and application to basic modes of convection

Geophysical Journal International

Volumn 163, Issue 2, 2005, Pages 788-800

  Muhlhaus, Hans Bernd ^a,b   Regenauer Lieb, Klaus ^b  

^a UNIVERSITY OF QUEENSLAND   (Australia)

^b CSIRO   (Australia)

Author keywords

Co rotational; Convection; Deborah number; Plasticity; Visco elasticity

Indexed keywords

ELASTICITY; EULERIAN ANALYSIS; FINITE ELEMENT METHOD; GEODYNAMICS; MANTLE STRUCTURE; PLASTICITY; PLATE TECTONICS; STRESS; SUBDUCTION ZONE; VISCOELASTICITY;

EID: 33744938765     PISSN: 0956540X     EISSN: 1365246X     Source Type: Journal    
DOI: 10.1111/j.1365-246X.2005.02742.x     Document Type: Article

References (36)

1. Bercovici, D., 1993. A simple model of plate generation from mantle flow, Geophys. J. Int., 114, 635-650.
2. Biot, M., 1965. The Mechanics of Incremental Deformations, John Wiley, New York.
3. Braun, J., 1994. 3-dimensional numerical simulations of crustal-scale wrenching using a nonlinear failure criterion, Journal of Structural Geology, 16 (8), 1173-1186.
4. Funiciello, F., Morra, G., Regenauer-Lieb, K. & Giardini, D., 2003. Dynamics of retreating slabs: 1. Insights from two-dimensional numerical experiments, Journal of Geophysical Research-Solid Earth, 108 (B4), art. no.-2206.
5. Gruntfest, I.J., 1963. Thermal feedback in liquid flow; plane shear at constant stress, Transactions of the Society of Rheology, 8, 195-207.
6. Gurnis, M., Eloy, C. & Zhong, S.J., 1996. Free-surface formulation of mantle convection.2. Implication for subduction-zone observables, Geophys. J. Int., 127 (3), 719-727.
7. Harder, H., 1991. Numerical-simulation of thermal-convection with maxwellian viscoelasticity, Journal of Non-Newtonian Fluid Mechanics, 39 (1), 67-88.
8. Hill, R., 1998. The Mathematical Theory of Plasticity, Oxford University Press, Oxford.
9. Karato, S. & Wu, P., 1993. Rheology of the Upper Mantle: A Synthesis, Science 260, 771-778.
10. Kirby, S.H., 1983. Rheology of the Lithosphere, Reviews of Geophysics and Space Physics, 21, 1458-1487.
11. Kolymbas, D. & Herle, I., 2003. Shear and objective stress rates in hypoplasticity, International Journal for Numerical and Analytical Methods in Geomechanics, 27 (8), 733-744.
12. Leroy, Y.M. & Molinari, A., 1992. Stability of steady states in shear zones, J. Mech. Phys. Solids, 40, 181-212.
13. Malvern, L.E., 1969. Introduction to the Mechanics of a Continuous Medium, Prentice-Hall, New Jersey.
14. Melosh, H.J., 1978. Dynamic support of the outer rise, Geophys. Res. Lett., 5, 321-324.
15. Moresi, L. & Solomatov, V., 1998. Mantle convection with a brittle lithosphere: Thoughts on the global tectonic styles of the Earth and Venus, Geophys J. Int., 133 (3), 669-682.
16. Moresi, L., Dufour, F. & Muhlhaus, H., 2002. Mantle convection models with viscoelastic/brittle lithosphere: Numerical methodology and plate tectonic modeling, Pageoph, 159 (9), 2335-2356.
17. Morra, G. & Regenauer-Lieb, K., 2005. A coupled solid-fluid method for modelling subduction, Philosophical magazine, London, in press.
18. Muhlhaus, H.B., 1985. Surface instability of a half space with bending stiffness (in German), Ing. Archive, 56, 383-388.
19. Needleman, A., 1988. Material rate dependence and mesh sensitivity in localization problems. Comput. Methods Appl. Mech. Engrg., 67, 69-85.
20. Ogawa, M., 2003. 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), 2067-2072.
21. Parmentier, E.M., Turcotte, D.L. & Torrance, K.E., 1976. Studies of finite amplitude non-Newtonian thermal convection with application to convection in the Earth mantle, J. geophys. Res., 81, 1839-1846.
22. Phan-Thien, N., 2002. Understanding Viscoelasticity-Basics of Rheology, Springer Verlag, Berlin Heidelberg New York.
23. Poliakov, A., Podladchikov, Y., Dawson, E. & Talbot, C.J., 1996. Salt diapirism with simultaneous brittle faulting and viscous flow, Geological Society, 100, 291-302.
24. Prager, W., 1961. Introduction to Mechanics of Continua, Boston, MA: Ginn.
25. Regenauer-Lieb, K. & Yuen, D.A., 2004. Positive feedback of interacting ductile faults from coupling of equation of state, rheology and thermal-mechanics, Phys. Earth planet. Int., 142 (1-2), 113-135.
26. Regenauer-Lieb, K., Yuen, D. & Branlund, J., 2001. The initation of subduction: Criticality by addition of water?, Science, 294, 578-580.
27. Schmalholz, S.M. & Podladchikov, Y., 1999. Buckling versus folding: importance of viscoelasticity. Geophys. Res. Lett., 26 (17), 2641-2644.
28. Scholz, C.H., 1990. The Mechanics of Earthquakes and Faulting, Cambridge University Press, Cambridge.
29. Solomatov, V., 1995. Scaling of temperature-dependent and stress-dependent viscosity convection. Physics of Fluids, 7 (2), 266-274.
30. Stein, C.A., Schmalzl, J. & Hansen, U., 2004. The effect of rheological parameters on plate behaviour in a self-consitent model of mantle convection, Phys. Earth planet. Int., 142(3-4), 225-255.
31. Tackley, P., 1998. Self-consistent generation of tectonic plates in three-dimensional mantle convection, Earth planet. Sci. Lett., 157, 9-22.
32. Tackley, P., 2000a. Self-consistent generation of tectonic plates in time- dependent, three-dimensional mantle convection simulations, 1. Pseudoplastic yielding, G3, 01 (23), 1525.
33. Tackley, P., 2000b. Self-consistent generation of tectonic plates in time- dependent, three-dimensional mantle convection simulations. 2. Strain weakening and asthenosphere, G3, 01 (25), 2027.
34. Trompert, R. & Hansen, U., 1998. Mantle convection simulations with rheologies that generate plate-like behavior, Nature, 395, 686-689.
35. Turcotte, D.L. & Schubert, G., 2002. Geodynamics, 2nd edn, Cambridge University Press, Cambridge.
36. Zienkiewicz, O.C. & Taylor, R.L., 2000. The Finite Element Method, 5th edn, Butterworth/Heinemann, Oxford, ISBN 0 7506 5050 8, 3.