Continuum damage mechanics for the lithosphere

Journal of Geophysical Research: Solid Earth

Volumn 116, Issue 4, 2011, Pages

  Karrech, A ^a,b   Regenauer Lieb, K ^a,b,c   Poulet, T ^a,b,c  

^a CSIRO   (Australia)

^b UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

^c Western Australian Geothermal Centre of Excellence   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; CONTINUUM DAMAGE MECHANICS; HIGH TEMPERATURE; LITHOSPHERIC STRUCTURE; LOADING; NUMERICAL METHOD; RHEOLOGY; VISCOPLASTICITY;

EID: 79954511301     PISSN: 21699313     EISSN: 21699356     Source Type: Journal    
DOI: 10.1029/2010JB007501     Document Type: Article

References (54)

1. Abaqus, Inc. (2007), User manual, version 6.4
2. Pawtucket, R. I. Bercovici, D. (1998), Generation of plate tectonics from lithosphere-mantle flow and void-volatile self-lubrication, Earth Planet. Sci. Lett., 154, 139-151, doi:10.1016/S0012-821X(97)00182-9.
3. Bercovici, D., and Y. Ricard (2003), Energetics of a two-phase model of lithospheric damage, shear localization and plate-boundary formation, Geophys. J. Int., 152, 581-596, doi:10.1046/j.1365-246X.2003.01854.x. (Pubitemid 36333834)
4. Bonora, N. (1997), A nonlinear CDM model for ductile failure, Eng. Fract. Mech., 58, 11-28, doi:10.1016/S0013-7944(97)00074-X.
5. Braeck, S., and Y. Podladchikov (2007), Spontaneous thermal runaway as an ultimate failure mechanism of materials, Phys. Rev. Lett., 98, 095504, doi:10.1103/PhysRevLett.98.095504. (Pubitemid 46363381)
6. Carosio, A., K. Willam, and G. Etse (2000), On the consistency of visco-plastic formulations, Int. J. Solids Struct., 37, 7349-7369, doi:10.1016/ S0020-7683(00)00202-X.
7. Chaboche, J. L. (1987), Continuum damage mechanics: Present state and future trends, Nucl. Eng. Des., 105, 19-33, doi:10.1016/0029-5493(87) 90225-1. (Pubitemid 18553576)
8. Chang, T. C., C. H. Popelar, and G. Staab (1986), A damage model for creep crack growth, Int. J. Fract., 32, 157-168, doi:10.1007/BF00018350. (Pubitemid 17529126)
9. Cocks, A. C. F., and M. F. Ashby (1980), Intergranular fracture during power-law creep under multiaxial stresses, Met. Sci., 14, 395-402. (Pubitemid 11454799)
10. Cocks, A. C. F., and M. F. Ashby (1982), On creep fracture by void growth, Prog. Mater. Sci., 27, 189-244, doi:10.1016/0079-6425(82) 90001-9.
11. Coleman, B., and W. Noll (1963), The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Ration. Mech. Anal., 13, 167-178, doi:10.1007/BF01262690.
12. Dhar, S., R. Sethuraman, and P. M. Dixit (1996), A continuum damage mechanics model for void growth and microcrack initiation, Eng. Fract. Mech., 53, 917-928, doi:10.1016/0013-7944(95)00151-4. (Pubitemid 126398497)
13. Esposito, L., and N. Bonora (2009), Time-independent formulation for creep damage modeling in metals based on void and crack evolution, Mater. Sci. Eng. A, 510-511, 207-213, doi:10.1016/j.msea.2008.06.052.
14. Fusseis, F., K. Regenauer-Lieb, J. Liu, R. Hough, and F. deCarlo (2009), Creep cavitation can establish a granular fluid pump through the middle crust, Nature, 459, 974-977, doi:10.1038/nature08051.
15. Goetze, C. (1978), The mechanisms of creep in olivine, Philos. Trans. R. Soc. London, 288, 99-119, doi:10.1098/rsta.1978.0008.
16. Halphen, B., and Q. S. Nguyen (1975), On generalized standard materials, J. Mec., 14, 39-63.
17. Hamiel, Y., V. Lyakhovsky, and A. Agnon (2004a), Coupled evolution of damage and porosity in poroelastic media: Theory and applications to deformation of porous rocks, Geophys. J. Int., 156, 701-713, doi:10.1111/j.1365-246X.2004. 02172.x. (Pubitemid 38398627)
18. Hamiel, Y., V. Lyakhovsky, Y. Ben-Zion, and D. Lockner (2004b), A viscoelastic damage model with applications to stable and unstable fracturing, Geophys. J. Int., 159, 1155-1165, doi:10.1111/j.1365-246X.2004.02452.x. (Pubitemid 39660986)
19. Hieronymous, C. (2004), Control on seafloor spreading geometries by stress- and strain-induced lithospheric weakening, Earth Planet. Sci. Lett., 222(1), 177-189, doi:10.1016/j.epsl.2004.02.022. (Pubitemid 38571199)
20. Hobbs, B. E., H. Mühlhaus, and A. Ord (1990), Instability, softening and localization of deformation, Geol. Soc. Spec. Publ., 54, 143-165, doi:10.1144/GSL.SP.1990.054.01.15.
21. Huang, H., and L. Xue (2009), Prediction of slant ductile fracture using damage plasticity theory, Int. J. Press. Vessels Piping, 86, 319-328, doi:10.1016/j.ijpvp.2008.11.027.
22. Kachanov, L. M. (1986), Introduction to Continuum Damage Mechanics, Martinus Nijhoff, Boston, Mass.
23. Kang, G. (2004), A visco-plastic constitutive model for ratcheting of cyclically stable materials and its finite element implementation, Mech. Mater., 36, 299-312, doi:10.1016/S0167-6636(03)00024-3.
24. Karrech, A., and A. Seibi (2010), Analytical model for the expansion of tubes under tension, J. Mater. Process. Technol., 210(2), 356-362, doi:10.1016/j.jmatprotec.2009.09.024.
25. Karrech, A., K. Regenauer-Lieb, and T. Poulet (2011a), Frame indifferent elastoplasticity of frictional materials at finite strain, Int. J. Solids Struct., 48, 397-407, doi:10.1016/j.ijsolstr.2010.09.026.
26. Karrech, A., A. Seibi, and D. Duhamel (2011b), Finite element modeling of rate-dependent ratcheting in granular materials, Comput. Geotech., 38, 105-112, doi:10.1016/j.compgeo.2010.08.012.
27. Kumar, Q. P., and V. Nukala (2006), A return mapping algorithm for cyclic viscoplastic constitutive models, Comput. Methods Appl. Mech. Eng., 195, 148-178, doi:10.1016/j.cma.2005.01.009. (Pubitemid 41511566)
28. Landuyt, W., and D. Bercovici (2009), Formation and structure of litho-spheric shear zones with damage, Phys. Earth Planet. Inter., 175(3-4), 115-126, doi:10.1016/j.pepi.2009.03.005.
29. Lemaitre, J. (1985), Coupled elasto-plasticity and damage constitutive equations, Comput. Methods Appl. Mech. Eng., 51, 31-49, doi:10.1016/0045- 7825(85)90026-X.
30. Lemaitre, J., and J. Chaboche (2001), Mécanique des Matériaux Solides, Duond, Paris.
31. Lemaitre, J., and J. Dufailly (1987), Damage measurements, Eng. Fract. Mech., 28, 643-661, doi:10.1016/0013-7944(87)90059-2.
32. Lyakhovsky, V., Z. Reches, R. Weinberger, and T. Scott (1997), Non-linear elastic behavior of damaged rocks, Geophys. J. Int., 130, 157-166, doi:10.1111/j.1365-246X.1997.tb00995.x.
33. Lyakhovsky, V., Y. Ben-Zion, and A. Agnon (2005), A viscoelastic damage rheology and rate- and state-dependent friction, Geophys. J. Int., 161, 179-190, doi:10.1111/j.1365-246X.2005.02583.x. (Pubitemid 40579094)
34. Mashayekhi, M., S. Ziaei-Rad, J. Parvizian, J. Niklewicz, and H. Hadavinia (2007), Ductile crack growth based on damage criterion: Experimental and numerical studies, Mech. Mater., 39, 623-636, doi:10.1016/j. mechmat.2006.10.004. (Pubitemid 46367318)
35. Mei, S., and D. L. Kohlstedt (2000a), Influence of water on plastic deformation of olivine aggregates: 1. Diffusion creep regime, J. Geophys. Res., 105(B9), 21,457-21,469, doi:10.1029/2000JB900179.
36. Mei, S., and D. L. Kohlstedt (2000b), Influence of water on plastic deformation of olivine aggregates: 2. Dislocation creep regime, J. Geophys. Res., 105(B9), 21,471-21,481, doi:10.1029/2000JB900180.
37. Nanjo, K., D. L. Turcotte, and R. Shcherbakov (2005), A model of damage mechanics for the deformation of the continental crust, J. Geophys. Res., 110, B07403, doi:10.1029/2004JB003438. (Pubitemid 41358552)
38. Paulino, G. H., and Y. Liu (2001), Implicit consistent and continuum tangent operators in elastoplastic boundary element formulation, Comput. Methods Appl. Mech. Eng., 190, 2157-2179, doi:10.1016/S0045-7825 (00)00228-0. (Pubitemid 32333701)
39. Perzyna, P. (1966), Fundamental problem in viscoplasticity, Adv. Appl. Mech., 35, 244-368.
40. Ponthot, J. (1995), Radial return extensions for visco-plasticity and lubricated friction, paper presented at International Conference on Structural Mechanics and Reactor Technology SMiRT-13, Sch. of Eng., Fed. Univ. of Rio Grande do Sul, Porto Alegre, Brazil.
41. Regenauer-Lieb, K. (1998), Dilatant plasticity applied to alpine collision: Ductile void growth in the intraplate area beneath the Eifel volcanic field, J. Geodyn., 27, 1-21, doi:10.1016/S0264-3707(97)00024-0. (Pubitemid 29099301)
42. Regenauer-Lieb, K. (2006), Water and geodynamics, Rev. Mineral. Geochem., 62, 451-473, doi:10.2138/rmg.2006.62.19. (Pubitemid 44541147)
43. Regenauer-Lieb, K., and D. Yuen (1998), Rapid conversion of elastic energy into plastic shear heating during incipient necking of the litho-sphere, Geophys. Res. Lett., 25, 2737-2740, doi:10.1029/98GL02056. (Pubitemid 29126175)
44. Regenauer-Lieb, K., D. A. Yuen, and J. Branlund (2001), The initiation of subduction: Criticality by addition of water, Science, 294, 578-580, doi:10.1126/science.1063891. (Pubitemid 32999551)
45. Regenauer-Lieb, K., R. F. Weinberg, and G. Rosenbaum (2006), The effect of energy feedbacks on continental strength, Nature, 442, 67-70, doi:10.1038/nature04868. (Pubitemid 44064209)
46. Regenauer-Lieb, K., G. Rosenbaum, and R. F. Weinberg (2008), Strain localisation and weakening of the lithosphere during extension, Tectonophysics, 458(1-4), 96-104, doi:10.1016/j.tecto.2008.02.014.
47. Regenauer-Lieb, K., A. Karrech, H. T. Chua, F. G. Horowitz, and D. Yuen (2010), Time-dependent, irreversible entropy production and geody-namics, Philos. Trans. R. Soc. A, 368, 285-300, doi:10.1098/ rsta.2009.0204.
48. Ricard, Y., D. Bercovici, and G. Schubert (2001), A two-phase model for compaction and damage: 2. Spplications to compaction, deformation, and the role of interfacial surface tension, J. Geophys. Res., 106(B5), 8907-8924, doi:10.1029/2000JB900431.
49. Sengupta, A. (2010), Strain localization in geomaterials in nature, laboratory tests and numerical analyses, Curr. Sci., 98(9), 1195-1201.
50. Simo, J. C., and R. L. Taylor (1985), Consistant tangent operators for rate- dependent elastoplasticity, Comput. Methods Appl. Mech. Eng., 48, 101-118, doi:10.1016/0045-7825(85)90070-2. (Pubitemid 15465636)
51. Steglich, D., A. Pirondi, N. Bonora, and W. Brocks (2005), Micromecha-nical modelling of cyclic plasticity incorporating damage, Int. J. Solids Struct., 42, 337-351, doi:10.1016/j.ijsolstr.2004.06.041.
52. Teng, X. (2008), Numerical prediction of slant fracture with continuum damage mechanics, Eng. Fract. Mech., 75, 2020-2041, doi:10.1016/j. engfracmech.2007.11.001.
53. Voyiadjis, G. Z., and F. H. Abed (2006), A coupled temperature and strain rate dependent yield function for dynamic deformations of bcc metals, Int. J. Plast., 22, 1398-1431, doi:10.1016/j.ijplas.2005.10.005.
54. Ziegler, H. (1977), An Introduction to Thermomechanics, North Holland, Netherlands.