Gradient plasticity modeling of geomaterials in a meshfree environment. Part I: Theory and variational formulation

Mechanics Research Communications

Volumn 32, Issue 5, 2005, Pages 536-546

  Manzari, Majid T ^a   Regueiro, Richard A ^b  

^a GEORGE WASHINGTON UNIVERSITY   (United States)

^b SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

Constitutive modeling; Geomaterials; Gradient plasticity; Meshfree analysis; Strain localization

Indexed keywords

GRAIN SIZE AND SHAPE; INTEGRAL EQUATIONS; KINEMATICS; NUMERICAL ANALYSIS; PLASTICITY; ROCK MECHANICS; STRAIN RATE; STRENGTH OF MATERIALS;

CONSTITUTIVE MODELING; GEOMATERIALS; GRADIENT PLASTICITY; MESHFREE ANALYSIS; STRAIN LOCALIZATION;

PLASTIC DEFORMATION;

EID: 21244453960     PISSN: 00936413     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mechrescom.2005.02.013     Document Type: Article

References (24)

1. E.C. Aifantis The physics of plastic deformation Int. J. Plast. 3 1987 2111 2248
2. H. Askes, and E.C. Aifantis Numerical modeling of size effects with gradient elasticity: formulation, meshless discretization, and examples Int. J. Fract. 117 2002 347 358
3. T. Belytschko, J. Fish, and B.E. Engelmann A finite element with embedded localization zones Comput. Methods Appl. Mech. Eng. 70 1988 59 89
4. M.D. Bolton The strength and dilatancy of sands Geotechnique 36 1 1986 65 78
5. R.I. Borja, and R.A. Regueiro Strain localization in frictional materials exhibiting displacement jumps Comput. Methods Appl. Mech. Eng. 190 2001 2555 2580
6. E. Cosserat, and F. Cosserat Theorie des Corps Deformables 1909 Herman et fils Paris
7. O.W. Dillon, and J. Kratochvil A strain gradient theory of plasticity Int. J. Solids Struct. 6 1970 1513 1533
8. A.C. Eringen, and D.G.B. Edelen On nonlocal elasticity Int. J. Eng. Sci. 10 1972 233 248
9. N.A. Fleck, and J.W. Hutchinson A phenomenological theory for strain gradient effects in plasticity J. Mech. Phys. Solids 41 1993 1825 1857
10. W.K. Liu, S. Jun, and Y.F. Zhang Reproducing kernel particle method Int. J. Numer. Methods Eng. 20 1995 1081 1106
11. M.T. Manzari Application of micropolar plasticity to post failure analysis in geomechanics Int. J. Anal. Numer. Methods Geomech. 28 2004 1011 1032
12. M.T. Manzari, and M.A. Nour Significance of soil dilatancy in slope stability analysis ASCE J. Geotech. Geo-environ. Eng. 126 1 2000 75 81
13. R.D. Mindlin Microstructure in linear elasticity Arch. Ration. Mech. Anal. 16 1964 51 78
14. R.D. Mindlin, and H.F. Tiersten Effects of couple-stresses in linear elasticity Arch. Ration. Mech. Anal. 11 5 1963 415 448
15. H.B. Muhlhaus, and E.C. Aifantis A variational principle for gradient plasticity Int. J. Solids Struct. 28 1991 845 857
16. H.B. Muhlhaus, and I. Vardoulakis The thickness of shear bands in granular materials Geotechnique 37 1987 271 283
17. M. Ortiz, Y. Leroy, and A. Needleman A finite element method for localized failure analysis Comput. Methods Appl. Mech. Eng. 61 1987 189 194
18. R.A. Regueiro, and R.I. Borja Plane strain finite element analysis of pressure sensitive plasticity with strong discontinuity Int. J. Solids Struct. 38 21 2001 3647 3672
19. J.C. Simo, J. Oliver, and F. Armero An analysis of strong discontinuity by strain softening in rate-independent inelastic solids Comput. Mech. 12 1993 277 296
20. I. Stakgold Green's Functions and Boundary Value Problems 1998 Wiley New York
21. Z. Tang, S. Shen, and S.N. Atluri Analysis of materials with strain-gradient effects: a meshless local Petrov-Galerkin (MLPG) approach, with nodal displacements only Comput. Model Eng. Sci. 4 1 2003 177 196
22. K. Terzaghi, R.B. Peck, and G. Mesri Soil Mechanics in Engineering Practice third ed. 1996 Wiley Interscience New York
23. I. Vardoulakis, G. Exadaktylos, and E. Aifantis Gradient elasticity with surface energy. Mode III crack problem Int. J. Solids. Struct. 33 3 1996 4531 4559
24. A. Zervos, X. Papanastasiou, and I. Vardoulakis A finite element displacement formulation Int. J. Numer. Methods Eng. 50 2001 1369 1388