A meshless formulation for geodynamic modeling

Journal of Geophysical Research: Solid Earth

Volumn 108, Issue 11, 2003, Pages

  Hansen, D L ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Computational methods; Continuum mechanics; Geodynamics; Meshless

Indexed keywords

CONTINUUM MECHANICS; GEODYNAMICS; MODELING;

EID: 1642368432     PISSN: 21699313     EISSN: 21699356     Source Type: Journal    
DOI: None     Document Type: Article

References (42)

1. Aris, R., Vectors, Tensors, and the Basic Equations of Fluid Mechanics. Prentice-Hall, Old Tappan, N. J., 1962.
2. Beissel. S., and T. Belytschko, Nodal integration of the element-free galerkin method, Comput. Methods Appl. Mech. Eng., 139, 49-74, 1996.
3. Belytschko, T., and S. Xiao, Stability analysis of particle methods with corrected deriviatives, Comput. Math. Appl., 43, 329-350, 2002.
4. Belytschko, T., Y. Lu, and L. Gu, Element-free galerkin methods, Int. J. Numer. Methods Eng., 37, 229-256, 1994.
5. Belytschko, T., Y. Krongauz, D. Organ, and P. Krysl, Mesh-less methods: An overview and recent developments. Comput. Methods Appl. Mech. Eng., 139, 3-47, 1996.
6. Bisshopp, K. E., and D. C. Drucker, Large deflection of cantilever beam, Q. Appl. Math, 3, 272-275, 1945.
7. Chen, J.-S., C. Pan, C.-T. Wu, and W. K. Liu, Reproducing kernel particle methods for large deformation analysis of non-linear structures, Comput. Methods Appl. Mech. Eng., 139, 195-227, 1996.
8. de Borst, R., Numerical modelling of bifurcation and localization in cohesive-frictional materials, Pure Appl. Geophys., 137, 367-390, 1991.
9. Gerbault, M., A. N. B. Poliakov, and M. Daignieres, Prediction of faulting from the theories of elasticity and plasticity: What are the limits?, J. Struct. Geol., 20, 301-320, 1998.
10. Gray, J., J. Monaghan, and R. Swift, SPH elastic dynamamics, Comput. Methods Appl. Mech. Eng., 190, 6641-6662, 2001.
11. Green, A. E., and W. Zerna. Theoretical Elasticity. Oxford Univ. Press, New York, 1968.
12. Hobbs, B. E., H. B. Mühlhaus, and A. Ord, Instability, softening and localization of deformation, in Deformation Mechanisms, Rheology, and Tectonics, edited by R. Knipe and E. Rutter, Geol. Soc. Spec. Publ., 54, 143-165, 1990.
13. Hutchinson, J. W., Finite strain analysis of elaslic-plastic solids and structures, in Numerical Solution of Nonlinear Structural Problems, edited by R. F. Hartung, pp. 17-29, Am. Soc. of Mech. Eng., New York, 1973.
14. Khan, A. S., and A. Huang, Continuum Theory of Plasticity, John Wiley, Hoboken, N. J., 1995.
15. Krongauz, Y., and T. Belytschko, Enforcement of essential boundary conditions in meshless approximations using finite elements, Comput. Methods Appl. Mech. Eng., 131, 133-145, 1996.
16. Lancaster, P., and K. Salkaukas, Surfaces generated by moving least-squares methods, Math. Comput., 37, 141-158, 1981.
17. Li, S., and W. K. Liu, Numerical simulations of strain localization in inelastic solids using mesh-free methods, Int. J. Numer. Methods Eng., 48, 1285-1309, 2000.
18. Liu, W. K., J. Adee, and S. Jun, Reproducing kernel particle methods for elastic and plastic problems. in Advanced Computational Methods for Material Modeling, AMD Ser., vol. 180, and PVD Ser., vol. 268, edited by B. J. Benson and R. A. Asaro, pp. 175-190. Am. Soc. of Mech. Eng., New York, 1993.
19. Liu, W. K., S. Jun, S. Li, J. Adee, and T. Belytschko, Reproducing kernel particle methods for structural dynamics. Int. J. Numer. Methods Eng., 38, 1655-1679, 1995.
20. Lu, Y. Y., T. Belytschko, and L. Gu, A new implementation of the element free galerkin methods, Comput. Methods Appl. Mech. Eng., 113, 397-414, 1994.
21. Lucy, L., A numerical approach to testing the fission hypothesis. J. Astron., 82, 1013-1024, 1977.
22. Malvern, L. E., Introduction to the Mechanics of a Continuous Medium, Prentice-Hall, Old Tappan, N. J., 1969.
23. Monaghan, J. J., An introduction to SPH, Comput. Phys. Comm., 48, 89-96, 1988.
24. Monaghan, J. J., SPH without a tensile instability, J. Comput. Phys., 159, 290-311, 2000.
25. Mühlhaus, H.-B., Application of cosserat theory in numerical solutions of limit load problems, Ing. Arch., 59, 124-137, 1989.
26. Mühlhaus, H.-B., and I. Vardoulakis, The thickness of shear bands in granular matrials. Geotechnique, 37, 271-283, 1987.
27. Nadai, A., Theory of Flow and Fracture of Solids, McGraw-Hill, New York, 1950.
28. Needleman, A., Non-normality and bifurcation in plane strain tension and compression, J. Mech. Phys. Solids, 27, 231-254, 1979.
29. Needleman, A., Material rate dependent and mesh sensitivity in localization problems, Comput. Methods Appl. Mech. Eng., 67, 68-85, 1988.
30. Pamin, J., and R. de Borst, Numerical simulation of localization phenomena using gradient plasticity and finite elements, Heron, 40, 71-92, 1995.
31. Ranalli, G., Rheology of the Earth, Chapman and Hall, New York, 1995.
32. Rodriguez-Ferran, A., P. Pegon, and A. Huerta, Two stress update algorithms for large strain: Accuracy analysis and numerical implementation, Int. J. Numer. Methods Eng., 40, 4363-4404, 1997.
33. Rudnicki, J. W., and J. R. Rice, Conditions of the localization of the deformation in pressure-sensitive materials, J. Mech. Phys. Solids, 23, 371-394, 1973.
34. Simo, J., and T. Hughes, Computational Inelasticity, Springer-Verlag, New York, 1998.
35. Timoshenko, S. P., and J. Gere, Mechanics of Materials, Van Nostrand Reinhold, Hoboken, N. J., 1972.
36. Tvergaard, V., Influence of voids on shear band instabilities under plane strain conditions, Int. Fract. Mech., 17, 389-407, 1981.
37. Twiss, R. J., and E. M. Moores. Structural Geology, W. H. Freeman, New York, 1992
38. Vermeer, P. A., The orientation of shear bands in bi-axial tests. Geotechnique, 40, 223-236, 1990.
39. Vermeer, P. A., and R. de Borst, Non-associated plasticity for soils, concrete and rock, Heron, 29, 1-62, 1984.
40. Wang, W. M., L. J. Sluys, and R. de Borst, Interaction between material length scale and imperfection size for localisation phenomena in viscoplastic media, Eur J. Mech., A Solids, 15, 447-464, 1996.
41. Wang, W. M., L. J. Sluys, and R. de Borst, Viscoplasticity for instabilities due to strain softening and strain-rate softening, Int. J. Numer. Methods Eng., 40, 3839-3864, 1997.
42. Zienkiewicz, O. C., The Finite Element Method, 3rd ed., McGraw-Hill, New York, 1977.