SLIM3D: A tool for three-dimensional thermomechanical modeling of lithospheric deformation with elasto-visco-plastic rheology

Physics of the Earth and Planetary Interiors

Volumn 171, Issue 1-4, 2008, Pages 55-75

  Popov, A A ^a   Sobolev, S V ^a  

^a GFZ GERMAN RESEARCH CENTRE FOR GEOSCIENCES   (Germany)

Author keywords

3D numerical modeling; Geodynamics; Lithospheric deformation; Mohr Coulomb; Strain localization

Indexed keywords

ABS RESINS; BOUNDARY VALUE PROBLEMS; CODES (SYMBOLS); COLLOIDS; COMPRESSION TESTING; COMPUTER PROGRAMMING LANGUAGES; DEFORMATION; ELASTICITY; FORMING; MODELS; OBJECT ORIENTED PROGRAMMING; PLASTICITY; PLASTICS; RHEOLOGY; THERMOMECHANICAL TREATMENT; VISCOSITY;

3D NUMERICAL MODELING; GEODYNAMICS; LITHOSPHERIC DEFORMATION; MOHR-COULOMB; STRAIN LOCALIZATION;

THREE DIMENSIONAL;

BENCHMARKING; BOUNDARY CONDITION; COULOMB CRITERION; CREEP; DEFORMATION MECHANISM; EULERIAN ANALYSIS; GEODYNAMICS; LAGRANGIAN ANALYSIS; LINEAR PROGRAMING; LITHOSPHERIC STRUCTURE; MOHR THEORY; NUMERICAL MODEL; RHEOLOGY; THREE-DIMENSIONAL MODELING;

EID: 55749091485     PISSN: 00319201     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.pepi.2008.03.007     Document Type: Article

References (82)

1. Adams M.F. Parallel multigrid solvers for 3D unstructured finite element problems in large deformation elasticity and plasticity. Int. J. Numer. Methods Eng. 48 (2000) 1241-1262
2. Alejano L.R., and Alonso E. Considerations of the dilatancy angle in rocks and rock masses. Int. J. Rock Mech. Min. Sci. 42 (2005) 481-507
3. Amestoy P.R., Duff I.S., and L'Excellent J.-Y. Multifrontal parallel distributed symmetric and unsymmetric solvers. Comput. Methods Appl. Mech. Eng. 184 (2000) 501-520
4. Arthur J.R.F., Dunstan T., Al-Ani Q.A.J., and Assadi A. Plastic deformation and failure of granular media. Geotechnique 27 (1977) 53-74
5. Babeyko A.Yu., Sobolev S.V., Trumbull R.B., Oncken O., and Lavier L.L. Numerical models of crustal scale convection and partial melting beneath the Altiplano-Puna plateau. Earth Planet. Sci. Lett. 199 (2002) 373-388
6. Babuska I. The finite element method with Lagrangian multipliers. Numeric. Math. 20 (1973) 179-192
7. Bailey R.C. Large time step numerical modelling of the flow of Maxwell materials. Geophys. J. Int. 164 (2006) 460-466
8. Bathe K.J., Ramm E., and Wilson E.L. Finite element formulations for large deformation dynamic analysis. Int. J. Numer. Methods Eng. 9 (1975) 353-386
9. Belytschko T., and Tabbara M. H-adaptive finite element methods for dynamic problems, with emphasis on localization. Int. J. Numer. Methods Eng. 36 (1993) 4245-4265
10. Belytschko T., Liu W.K., and Moran B. Nonlinear Finite Elements for Continua and Structures (2000), John Wiley & Sons, Chichester
11. Bercovici D. A simple model of plate generation from mantle flow. Geophys. J. Int. 114 (1993) 635-650
12. Blake A. Handbook of Mechanics, Materials, and Structures (1985), Wiley, New York
13. Bonet J., and Wood R.D. Nonlinear Continuum Mechanics for Finite Element Analysis (1997), Cambridge University Press, Cambridge
14. Bonet J., Marriott H., and Hassan O. An averaged nodal deformation gradient linear tetrahedral element for large strain explicit dynamic applications. Commun. Numer. Methods Eng. 17 (2001) 551-561
15. Borja R.I., and Aydin A. Computational modeling of deformation bands in granular media. Part I. Geological and mathematical framework. Comput. Methods Appl. Mech. Eng. 193 (2004) 2667-2698
16. Borja R.I., Sama K.M., and Sanz P.F. On the numerical integration of three-invariant elastoplastic constitutive models. Comput. Methods Appl. Mech. Eng. 192 (2003) 1227-1258
17. Brace F.W., and Kohlstedt D.L. Limits on lithospheric stress imposed by laboratory experiments. J. Geophys. Res. 50 (1980) 6248-6252
18. Braun J., and Sambridge M. Dynamical Lagrangian Remeshing (DLR): a new algorithm for solving large strain deformation problems and its application to fault propagation folding. Earth Planet. Sci. Lett. 124 (1994) 211-220
19. Brezzi F. On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers. RAIRO 8 (1974) 129-151
20. Buiter S.J.H., Babeyko A.Y., Ellis S., Gerya T.V., Kaus B.J.P., Kellner A., Schreurs G., and Yamada Y. The Numerical Sandbox: Comparison of Model Results for a Shortening and an Extension Experiment, Analogue and Numerical Modelling of Crustal-Scale Processes 253 (2006), Geological Society Special Publication, London pp. 29-64
21. Bunge H.-P., and Baumgardner J.R. Mantle convection modeling on parallel virtual machines. Comput. Phys. 9 (1995) 207-215
22. Christensen U., and Harder H. 3-D convection with variable viscosity. Geophys. J. Int. 104 (1991) 213-220
23. Coulomb C.A. Test on the applications of the rules of maxima and minima to some problems of statics related to architecture. Mem. Math. Phys. 7 (1773) 343-382 (in French)
24. Crisfield M.A. An arc-length method including line searches and accelerations. Int. J. Numer. Methods Eng. 19 (1983) 1269-1289
25. Ekevid T., Kettil P., and Wiberg N.-E. Adaptive multigrid for finite element computations in plasticity. Comput. Struct. 82 (2004) 2413-2424
26. Farhat C., Lesoinne M., and Pierson K. A scalable dual-primal domain decomposition method. Numer. Linear Algebra Appl. 7 (2000) 687-714
27. Fish J., and Shek K. Computational aspects of incrementally objective algorithms for large deformation plasticity. Int. J. Numer. Methods Eng. 44 (1999) 839-851
28. Flanagan D.P., and Belytschko T. A uniform strain hexahedron and quadrilateral with orthogonal hourglass control. Int. J. Numer. Methods Eng. 17 (1981) 679-706
29. Fullsack P. An arbitrary Lagrangian-Eulerian formulation for creping flows and its application in tectonic models. Geophys. J. Int. 120 (1995) 1-23
30. Geers M.G.D. Enhanced solution control for physically and geometrically non-linear problems. Part I. The subplane control approach. Int. J. Numer. Methods Eng. 46 (1999) 177-204
31. George A. Nested dissection of a regular finite element mesh. SIAM J. Numer. Anal. 10 (1973) 345-363
32. Gerya T.V., and Yuen D.A. Robust characteristics method for modelling multiphase visco-elasto-plastic thermo-mechanical problems. Phys. Earth Planet. Inter. 163 (2007) 83-105
33. Gupta A., Karypis G., and Kumar V. Highly scalable parallel algorithms for parse matrix factorization. IEEE Trans. Parallel Distrib. Syst. 8 (1997) 502-520
34. Harlow F., and Welsh J. Numerical calculation of time-dependant viscous incompressible flow of fluid with free surface. Phys. Fluids 8 (1965) 2182-2189
35. Hestenes M.R., and Stiefel E. Methods of conjugate gradients for solving linear systems. J. Res. Nat. Bur. Stand. 49 (1952) 409-436
36. Hirt C.W., Amsden A.A., and Cook J.L. An arbitrary Lagrangian-Eulerian computing method for all flow speeds. J. Comput. Phys. 14 (1974) 227-253
37. Hughes T.J.R. The Finite Element Method (1987), Prentice-Hall, Englewood-Cliffs, New Jersey
38. Hughes T.J.R., and Winget J. Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis. Int. J. Numer. Methods Eng. 15 (1980) 1862-1867
39. Kameyama M., Yuen D.A., and Karato S.-I. Thermal-mechanical effects of low-temperature plasticity (the Peierls mechanism) on the deformation of a viscoelastic shear zone. Earth Planet. Sci. Lett. 168 (1999) 159-172
40. Karato S.-I., Riedel M.R., and Yuen D.A. Rheological structure and deformation of subducted slabs in the mantle transition zone: implications for mantle circulation and deep earthquakes. Phys. Earth Planet. Inter. 127 (2001) 83-108
41. Kaus B.J.P., and Podladchikov Y.Y. Initiation of localized shear zones in viscoelastoplastic rocks. J. Geophys. Res. 111 (2006) B04412 10.1029/2005JB003652
42. Ladyzhenskaya O.A. The Mathematical Theory of Viscous Incompressible Flow. 2nd ed. (1969), Gordon & Breach, New York
43. Larsson R., and Runesson K. Implicit integration and consistent linearization for yield criteria of the Mohr-Coulomb type. Mech. Cohes. Frict. Mater. 1 (1996) 367-383
44. Liu W.K., Guo Y., Tang S., and Belytschko T. A multiple-quadrature eight-node hexahedral finite element for large deformation elastoplastic analysis. Comput. Methods Appl. Mech. Eng. 154 (1998) 69-132
45. Malkus D.S., and Hughes T.J.R. Mixed finite element methods-reduced and selective integration techniques: a unification of concept. Comput. Methods Appl. Mech. Eng. 15 (1978) 63-81
46. Moresi L.N., Dufour F., and Muhlhaus H. A Lagrangian integration point finite element method for large deformation modeling of viscoelastic geomaterials. J. Comput. Phys. 184 (2003) 476-497
47. Muhlhaus H.-B., and Aifantis E.C. A variational principle for gradient plasticity. Int. J. Solids Struct. 28 (1991) 845-857
48. Muhlhaus H.-B., and Regenauer-Lieb K. Towards a self-consistent plate mantle model that includes elasticity: simple benchmarks and application to basic modes of convection. Geophys. J. Int. 163 (2005) 788-800
49. Muhlhaus H.-B., and Vardoulakis I. The thickness of shear bands in granular materials. Geotechnique 37 (1987) 271-283
50. O'Neill C., Moresi L., Muller D., Albert R., and Dufour F. Ellipsis 3D: a particle-in-cell finite-element hybrid code for modelling mantle convection and lithospheric deformation. Comput. Geosci. 32 (2006) 1769-1779
51. Ortiz M., and Popov E.P. Accuracy and stability of integration algorithms for elastoplastic constitutive relations. Int. J. Numer. Methods Eng. 21 (1985) 1561-1576
52. Perez-Foguet A., Rodriguez-Ferran A., and Huerta A. Numerical differentiation for local and global tangent operators in computational plasticity. Comput. Methods Appl. Mech. Eng. 189 (2000) 277-296
53. Petrunin A., and Sobolev S.V. What controls thickness of sediments and lithospheric deformation at a pull-apart basin?. Geology 34 (2006) 389-392
54. Poliakov A.N., and Herrmann H.J. Self-organized criticality of plastic shear bands in rocks. Geophys. Res. Lett. 21 (1994) 2143-2146
55. Poliakov A.N., Cundall P.A., Podladchikov Y.Y., and Lyakhovsky V.A. An explicit inertial method for the simulation of the viscoelastic flow: an evaluation of elastic effects on diapiric flow in two- and three-layers models. In: Stone D.B., and Runcorn S.K. (Eds). Flow and Creep in the Solar System: Observations, Modelling and Theory (1993), Kluwer Academic Publishers 175-195
56. Press W.H., Teukolsky S.A., Vetterling W.T., and Flannery B.P. Numerical Recipes in C++: The Art of Scientific Computing. 2nd ed. (2002), Cambridge University Press, Cambridge
57. Puso M.A., and Solberg J. A stabilized nodally integrated tetrahedral. Int. J. Numer. Methods Eng. 67 (2006) 841-867
58. Rashid M.M. Incremental kinematics for finite element applications. Int. J. Numer. Methods Eng. 36 (1993) 3937-3956
59. Rassineux A. Generation and optimization of tetrahedral meshes by advancing front technique. Int. J. Numer. Methods Eng. 41 (1998) 651-674
60. Reese S. On a consistent hourglass stabilization technique to treat large inelastic deformations and thermo-mechanical coupling in plane strain problems. Int. J. Numer. Methods Eng. 57 (2003) 1095-1127
61. Regenauer-Lieb K. Water and geodynamics. Rev. Miner. Geochem. 62 (2006) 451-473
62. Regenauer-Lieb K., and Yuen D.A. Modeling shear zones in geological and planetary sciences: solid- and fluid-thermal-mechanical approaches. Earth Sci. Rev. 63 (2003) 295-349
63. Regenauer-Lieb K., and Yuen D.A. Positive feedback of interacting ductile faults from coupling of equation of state, rheology and thermal-mechanics. Phys. Earth Planet. Inter. 142 (2004) 113-135
64. Roscoe K.H. The influence of strains in soil mechanics, 10th Rankine Lecture. Geotechnique 20 (1970) 129-170
65. Saad Y. ILUT: a dual threshold incomplete ILU factorization. Numer. Linear Algebra Appl. 1 (1994) 387-402
66. Schmalholz S.M., Podladchikov Y.Y., and Schmid D.W. A spectral/finite difference method for simulating large deformations of heterogeneous, viscoelastic materials. Geophys. J. Int. 145 (2001) 199-208
67. Shampine, L.F., Watts, H.A., 1970. FZERO, a root-solving code. Report SC-TM-70-631. Sandia Laboratories.
68. Shephard M.S., and Georges M.K. Automatic three-dimensional mesh generation by the finite octree technique. Int. J. Numer. Methods Eng. 32 (1991) 709-749
69. Shih T.M., Tan C.H., and Hwang B.C. Effects of grid staggering on numerical schemes. Int. J. Numer. Methods Fluids 9 (1989) 193-212
70. Simo J.C., and Hughes T.J.R. Computational Inelasticity. 2nd ed. (2000), Springer-Verlag, New York
71. Simo J.C., and Taylor R.L. Consistent tangent operators for rate-independent elastoplasticity. Comput. Methods Appl. Mech. Eng. 48 (1985) 101-118
72. Simo J.C., Kennedy J.G., and Govindjee S. Non-smooth multisurface plasticity and viscoplasticity. Loading/unloading conditions and numerical algorithms. Int. J. Numer. Methods Eng. 26 (1988) 2161-2185
73. Slezkin A. Dynamics of Viscous Incompressible Fluid (1955), Gostekhizdat, Moscow (in Russian)
74. Sloan S.W., and Booker J.R. Removal of singularities in Tresca and Mohr-Coulomb yield functions. Commun. Appl. Numer. Methods 2 (1986) 173-179
75. Sobolev S.V., Petrunin A., Garfunkel Z., Babeyko A.Y., and Group DESERT. Thermo-mechanical model of the Dead Sea transformation. Earth Planet. Sci. Lett. 238 (2005) 78-95
76. Tackley P.J., and Xie S. STAG3D: a code for modeling thermo-chemical multiphase convection in Earth's mantle. In: Bathe K.J. (Ed). Proceedings of the Second MIT Conference on Computational Fluid and Solid Mechanics (2003), Elsevier B.V., Amsterdam 1524-1527
77. Trompert R.A., and Hansen U. The application of a finite-volume multigrid method to 3-dimensional flow problems in a highly viscous fluid with a variable viscosity. Geophys. Astrophys. Fluid Dyn. 83 (1996) 261-291
78. Vermeer P.A. The orientation of shear bands in biaxial tests. Geotechnique 40 (1990) 223-226
79. Weinberg R.B., and Schmeling H. Polydiapirs: multiwavelength gravity structures. J. Struct. Geol. 14 (1992) 425-436
80. Wilkins M.L. Calculation of elastic-plastic flow. In: Alder B. (Ed). Methods in Computational Physics (1964), Academic Press, New York 211-263
81. Zhong S., and Gurnis M. Incorporation of fault-bound plates in three-dimensional models of mantle flow. Nature 383 (1996) 245-247
82. Zienkiewicz O.C., and Taylor R.L. The Finite Element Method. 5th ed. (2000), Butterworth-Heinemann, Oxford