Numerical modeling of the motion of deformable ellipsoidal objects in slow viscous flows

Journal of Structural Geology

Volumn 29, Issue 3, 2007, Pages 435-452

  Jiang, Dazhi ^a  

^a UNIVERSITY OF WESTERN ONTARIO   (Canada)

Author keywords

Clast; Eshelby's theory; Fabric development; Numerical modeling; Preferred orientation; Rotation; Strain

Indexed keywords

ELLIPSOIDAL OBJECTS; ESHELBY THEORY; EULER ANGLES; POLAR COORDINATE ANGLES;

DEFORMATION; EULER EQUATIONS; GRAPHIC METHODS; GRAPHICAL USER INTERFACES; MATHEMATICAL MODELS; STRAIN RATE; VISCOUS FLOW;

STRUCTURAL GEOLOGY;

ALGORITHM; CLAST; DEFORMATION; NUMERICAL MODEL; PREFERRED ORIENTATION; STRAIN; VISCOUS FLOW;

EID: 33947164211     PISSN: 01918141     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsg.2006.09.009     Document Type: Article

References (62)

1. Arbaret L., Mancktelow N.S., and Burg J.-P. Effect of shape and orientation on rigid particle rotation and matrix deformation in simple shear flow. Journal of Structural Geology 23 (2001) 113-125
2. Başar Y., and Weichert D. Nonlinear Continuum Mechanics of Solids (2000), Springer, Berlin
3. Benedikt B., Lewis M., and Rangaswamy P. On elastic interactions between spherical inclusions by the equivalent inclusion method. Computational Materials Science 37 (2006) 380-392
4. Bilby B.A., Eshelby J.D., and Kundu A.K. The change of shape of a viscous ellipsoidal region embedded in a slowly deforming matrix having a different viscosity. Tectonophysics 28 (1975) 265-274
5. Bilby B.A., and Kolbuszewski M.L. The finite deformation of an inhomogeneity in two-dimensional slow viscous incompressible flow. Proceedings of the Royal Society of London A355 (1977) 335-353
6. Bretherton F.P. The motion of rigid particles in shear flow at low Reynolds number. Journal of Fluid Mechanics 14 (1962) 284-301
7. ten Brink C.E. Development of Porphyroclast Geometries during Non-Coaxial Flow. Geologica Ultraiectina vol. 142 (1996) 163
8. Ceriani S., Mancktelow N.S., and Pennacchioni G. Analogue modelling of the influence of shape and particle/matrix interface lubrication on the rotational behaviour of rigid particles in simple shear. Journal of Structural Geology 25 (2003) 2005-2021
9. Dunnet D. A technique of finite strain analysis using elliptical particles. Tectonophysics 7 (1969) 117-136
10. Eirich F., and Mark H. Ueber Lösungsmittelbindung durch Immobilisierung. Papierfabrikant 27 (1937) 251-258
11. Eshelby J.D. The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proceedings of the Royal Society of London A241 (1957) 376-396
12. Eshelby J.D. The elastic field outside an ellipsoidal inclusion. Proceedings of the Royal society of London A252 (1959) 561-569
13. Fletcher R.C. Anisotropic viscosity of a dispersion of aligned elliptical cylindrical clasts in viscous matrix. Journal of Structural Geology 26 (2004) 1977-1987
14. Freeman B. The motion of rigid ellipsoidal particles in slow flows. Tectonophysics 113 (1985) 163-183
15. Freeman B. The behavior of deformable ellipsoidal particles in three-dimensional slow flows: implications for geological strain analysis. Tectonophysics 132 (1987) 297-309
16. Gay N.C. Orientation of mineral lineation along the flow direction in rocks: a discussion. Tectonophysics 3 (1966) 559-564
17. Gay N.C. The motion of rigid particles embedded in a viscous fluid during pure shear deformation of the fluid. Tectonophysics 5 (1968) 81-88
18. Gay N.C. Pure shear and simple shear deformation of inhomogeneous viscous fluids. 1. Theory. Tectonophysics 5 (1968) 211-234
19. Ghosh S.K., and Ramberg H. Reorientation of inclusions by combination of pure shear and simple shear. Tectonophysics 34 (1976) 1-70
20. Goddard J.D., and Miller C. Nonlinear effects in the rheology of dilute suspensions. Journal of Fluid Mechanics 28 (1967) 657-673
21. Goldsmith H.L., and Mason S.G. The microrheology of dispersions. In: Eirich F.R. (Ed). Rheology, Theory and Applications vol. 4 (1967) 85-250
22. Ildefonse B., Launeau P., Bouchez J.-L., and Fernandez A. Effect of mechanical interactions on the development of shape preferred orientations: a two-dimensional experimental approach. Journal of Structural Geology 14 (1992) 73-83
23. Ildefonse B., and Mancktelow N.S. Deformation around rigid particle: influence of slip at the particle/matrix interface. Tectonophysics 221 (1993) 345-359
24. Ildefonse B., Sokoutis D., and Mancktelow N.S. Mechanical interactions between rigid particles in a deforming ductile matrix. Analogue experiments in simple shear flow. Journal of Structural Geology 14 (1992) 1253-1266
25. Jeffery G.B. The motion of ellipsoidal particles immersed in a viscous fluid. Proceedings of the Royal Society of London A102 (1922) 161-179
26. Jeffrey A. Handbook of Mathematical Formulas and Integrals (1995), Academic Press, New York
27. Jezek J., Melka R., Schulmann K., and Venera Z. The behaviour of rigid triaxial ellipsoidal particles in viscous flows - modeling of fabric evolution in a multiparticle system. Tectonophysics 229 (1994) 165-180
28. Jezek J., Schulmann K., and Segeth K. Fabric evolution of rigid inclusions during mixed coaxial and simple shear flows. Tectonophysics 257 (1996) 203-221
29. Jiang D. Vorticity decomposition and its application to sectional flow characterization. Tectonophysics 301 (1999) 243-259
30. Jiang, D. Numerical modeling of the motion of rigid ellipsoidal objects in slow viscous flows: a new approach. Journal of Structural Geology, in press.
31. Launeau P., and Cruden A.R. Magmatic fabric acquisition mechanisms in a syenite: results of a combined anisotropy of magnetic susceptibility and image analysis study. Journal of Geophysical Research 103 (1998) 5067-5089
32. Lee K.Y., and Paul D.R. A model for composites containing three-dimensional ellipsoidal inclusions. Polymer 46 (2005) 9064-9080
33. f/φ{symbol} Technique (1985), Pergamon Press, Oxford
34. Lister G.S. A vorticity equation for lattice reorientation during plastic deformation. Tectonophysics 82 (1982) 351-366
35. Lister G.S., and Williams P.F. The partitioning of deformation in flowing rock masses. Tectonophysics 92 (1983) 1-33
36. Liu X., and Hu G. Inclusion problem of microstretch continuum. International Journal of Engineering Science 42 (2004) 849-860
37. Ma H., Liu X., and Hu G. Overall elastoplastic property for micropolar composites with randomly oriented ellipsoidal inclusions. Computational Materials Science 37 (2006) 582-592
38. Mancktelow N.S., Arbaret L., and Pennacchioni G. Experimental observations on the effect of interface slip on rotation and stabilisation of rigid particles in simple shear and a comparison with natural mylonites. Journal of Structural Geology 24 (2002) 567-585
39. Mandal N., Samanta S.K., Bhattacharyya G., and Chakraborty C. Deformation of ductile inclusions in a multiple inclusion system in pure shear. Journal of Structural Geology 25 9 (2003) 1359-1370
40. Mandal N., Kumar Samanta S., Bhattacharyya G., and Chakraborty C. Rotation behaviour of rigid inclusions in multiple association: insights from experimental and theoretical models. Journal of Structural Geology 27 (2005) 679-692
41. Mandal N., Misra S., and Samanta S.K. Rotation of single rigid inclusions embedded in an anisotropic matrix: a theoretical study. Journal of Structural Geology 27 (2005) 731-743
42. March A. Mathematische Theorie der Regelung nach der Korngestalt bei affiner deformation. Zeitschrift für Kristallographie 81 (1932) 285-297
43. Marques F.O., and Bose S. Influence of a permanent low-friction boundary on rotation and flow in rigid inclusion/viscous matrix systems from an analogue perspective. Tectonophysics 382 (2004) 229-245
44. Marques F.O., and Coelho S. Rotation of rigid elliptical cylinders in viscous simple shear flow: analogue experiments. Journal of Structural Geology 23 (2001) 609-617
45. Masuda T., Michibayashi K., and Ohta H. Shape preferred orientation of rigid particles in a viscous matrix: reevaluation to determine kinematic parameters of ductile deformation. Journal of Structural Geology 17 (1995) 115-129
46. Mura T. Micromechanics of Defects in Solids (1987), Martinus Nijhoff Publishers, Dordrecht/Boston/Lancaster
47. Passchier C.W. Stable positions of rigid objects in non-coaxial flow - a study in vorticity analysis. Journal of Structural Geology 9 (1987) 679-690
48. Passchier C.W., and Simpson C. Porphyroclast systems as kinematic indicators. Journal of Structural Geology 8 (1986) 831-843
49. Ramsay J.G. Folding and Fracturing of Rocks (1967), McGraw-Hill Book Company, New York
50. Reed J.L., and Tryggvason E. Preferred orientation of rigid particles in a viscous matrix deformed by pure shear and simple shear. Tectonophysics 24 (1974) 85-98
51. Robertson C.R., and Acrivos A. Low Reynolds number shear flow past a rotating circular cylinder. Part 1: Momentum transfer. Journal of Fluid Mechanics 40 (1970) 685-704
52. Schmid D.W., and Podladchikov Y.Y. Are isolated stable rigid clasts in shear zones equivalent to voids?. Tectonophysics 384 (2004) 233-242
53. Schmid D.W., and Podladchikov Y.Y. Mantled porphyroclast gauges. Journal of Structural Geology 27 (2005) 571-585
54. Spencer A.J.M. Continuum Mechanics (1980), Longman, London
55. Taylor G.I. The motion of ellipsoidal particles immersed in a viscous fluid. Proceedings of the Royal Society of London A103 (1923) 58-61
56. Treagus S.H. Modelling the bulk viscosity of two-phase mixtures in terms of clast shape. Journal of Structural Geology 24 (2002) 57-76
57. Treagus S.H., and Treagus J.E. Effects of object ellipticity on strain, and implications for clast-matrix rocks. Journal of Structural Geology 23 (2001) 601-608
58. Treagus S.H., and Treagus J.E. Studies of strain and rheology of conglomerates. Journal of Structural Geology 24 (2002) 1541-1567
59. Trevelyan B.J., and Mason S.G. Particle motions in sheared suspensions. I. Rotations. Journal of Colloid Science 6 (1951) 354-367
60. Truesdell C.A., and Topin R.A. The classic field theory. In: Flügge S. (Ed). Encyclopedia of Physics. Principles of Classic Mechanics and Field Theory vol. III (1960), Springer-Verlag, Berlin 226-793
61. Tullis T.E. Experiments on the origin of slaty cleavage and schistosity. Geological Society of America Bulletin 87 (1976) 745-753
62. Willis D.G. A kinematic model of preferred orientation. Geological Society of America Bulletin 88 (1977) 883-894