Shear banding analysis of geomaterials by strain gradient enhanced damage model

International Journal of Solids and Structures

Volumn 42, Issue 20, 2005, Pages 5335-5355

  Zhao, Jidong ^a   Sheng, Daichao ^a   Zhou, Weiyuan ^b  

^a UNIVERSITY OF NEWCASTLE   (Australia)

^b TSINGHUA UNIVERSITY   (China)

Author keywords

Damage localization; Discontinuous bifurcation; Geomaterials; Second order characteristic surface; Strain gradient plasticity

Indexed keywords

BIFURCATION (MATHEMATICS); BOUNDARY CONDITIONS; BRITTLENESS; COMPUTER SIMULATION; MATHEMATICAL MODELS; PLASTICITY; POISSON RATIO; PROBLEM SOLVING; SHEAR DEFORMATION; SHEAR STRESS; STRAIN RATE;

DAMAGE LOCALIZATION; DISCONTINUOUS BIFURCATION; GEOMATERIALS; SECOND-ORDER CHARACTERISTIC SURFACE; STRAIN GRADIENT PLASTICITY;

MATERIALS SCIENCE;

EID: 21244446304     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2005.02.029     Document Type: Article

References (48)

1. E.C. Aifantis On the microstructural origin of certain inelastic models Trans. ASME J. Eng. Mater. Tech. 106 1984 326 330
2. E.C. Aifantis The physics of plastic deformation Int. J. Plast. 3 1987 211 247
3. E.C. Aifantis Gradient plasticity J. Lemaitre Handbook of materials behavior models 2001 Academic Press New York 291 307
4. E.C. Aifantis Update on a class of gradient theories Mech. Mater. 35 2003 259 280
5. O. Al Hattamleh, B. Muhunthan, and H.M. Zbib Gradient plasticity modelling of strain localization in granular materials Int. J. Numer. Anal. Meth. Geomech. 28 2004 465 481
6. H. Askes, and L.J. Sluys A classification of higher-order strain-gradient models in damage mechanics Arch. Appl. Mech. 73 2003 448 465
7. R. Chambon, D. Caillerie, and N. El Hassan One-dimensional localisation studied with a second grade model Eur. J. Mech. - A/Solids 17 4 1998 637 656
8. R. Chambon, D. Caillerie, and T. Matsuchima Plastic continuum with microstructure, local second gradient theories for geomaterials: Localization studies Int. J. Solids Struct. 38 2001 8503 8527
9. R. De Borst, and H.B. Mühlhaus Gradient dependent plasticity: Formulation and algorithmic aspects Int. J. Numer. Meth. Eng. 35 1992 521 539
10. R. De Borst, and E. Van der Giessen Material instabilities in solids 1998 John Wiley & Sons Chichester
11. N.A. Fleck, and J.W. Hutchinson A phenomenological theory for strain gradient effects in plasticity J. Mech. Phys. Solids 41 12 1993 1825 1857
12. N.A. Fleck, and J.W. Hutchinson Strain gradient plasticity J.W. Hutchinson T.Y. Wu Advances in applied mechanics vol. 33 1997 Academic Press New York 295 361
13. N.A. Fleck, and J.W. Hutchinson A reformulation of strain gradient plasticity J. Mech. Phys. Solids 49 2001 2245 2271
14. H. Gao, Y. Huang, W.D. Nix, and J.W. Hutchinson Mechanism-based strain gradient plasticity. I. Theory J. Mech. Phys. Solids 47 1999 1239 1263
15. P. Germain The method of virtual power in continuum mechanics. Part 2: microstructure SIAM J. Appl. Math. 25 3 1973 556 575
16. M.Y. Gutkin, and E.C. Aifantis Dislocations and disclinations in gradient elasticity Phys. Status Solidi 214B 1999 245 284
17. Hadamad, J., 1903. Lecons sur la propagation des ondes et les équations de l'hydrodynamique. Librarie Scientifique. A. Hermann, Paris
18. R. Hill A general theory of uniqueness and stability in elastic-plastic solids J. Mech. Phys. Solids 6 1958 236 249
19. C. Jaeger Rock mechanics and engineering 1979 Cambridge University Press New York
20. W. Koiter Couple-stress in the theory of elasticity Mech. Ser. B 2 1964 17 44
21. A. Konstantinidis, and E.C. Aifantis Recent developments in gradient plasticity. Part I: formulation and size effects J. Eng. Mater. Tech. 124 2002 358 364
22. E. Kuhl, and E. Ramm Simulation of strain localization with gradient with gradient enhanced damage models Comput. Mater. Sci. 16 2000 176 185
23. R.D. Mindlin Micro-structure in linear elasticity Arch. Rat. Mech. Anal. 16 1964 51 78
24. R.D. Mindlin Second gradient of strain and surface tension in linear elasticity Int. J. Solids Struct. 28 1965 845 857
25. H.B. Mühlhaus, and E.C. Aifantis A variational principle for gradient plasticity Int. J. Solids Struct. 28 1991 845 857
26. H.B. Mühlhaus, and I. Vardoulakis The thickness of shear bands in granular materials Géotechnique 37 1987 217 283
27. N.E. Ottosen, and K. Runesson Properties of discontinuous bifurcation solutions in elasto-plasticity Int. J. Solids Struct. 27 4 1991 401 421
28. G.L. Panger, J.L. Ding, H.M. Zbib, and E.C. Aifantis Measurement of shear band characteristics in low carbon steel using photoelasticity Scr. Metall. Mater. 25 1991 2103 2108
29. R.H.J. Peerlings, R. de Borst, W.A.M. Brekelmans, and J.H.P. Vree Gradient enhanced damage for quasi-brittle materials Int. J. Numer. Meth. Eng. 39 1996 3391 3404
30. S.T. Pietruszczak, and Z. Mroz Finite element analysis of deformation of strain softening materials Int. J. Numer. Meth. Eng. 17 1981 327 334
31. th Rankine lecture. Géotechnique 20(2), 129-170
32. J.W. Rudnicki The inception of faulting in a rockmass with a weakened zone J. Geophys. Res. 82 1977 844 854
33. J.W. Rudnicki, and J.R. Rice Conditions for the localization of deformation in pressure-sensitive dilatant materials J. Mech. Phys. Solids 23 1975 371 395
34. M.X. Shi, Y. Huang, and K.C. Hwang Plastic flow localization in mechanism-based strain gradient plasticity Int. J. Mech. Sci. 42 2000 2115 2131
35. J.Y. Shu, and N.A. Fleck Strain gradient crystal plasticity: size-dependent deformation of bicrystals J. Mech. Phys. Solids 47 1999 297 324
36. T. Thomas Plastic flow and fracture in solids 1961 Academic Press New York
37. R.A. Toupin Elastic materials with couple stresses Arch. Ration. Mech. Anal. 11 1962 385 414
38. N. Triantafyllidis, and E.C. Aifantis A gradient approach to localization of deformation. I. Hyperelastic materials J. Elast. 16 1986 225 238
39. I. Tsagrakis, and E.C. Aifantis Recent developments in gradient plasticity. Part I: formulation and size effects J. Eng. Mater. Tech. 124 2002 352 357
40. I. Tsagrakis, and E.C. Aifantis Element-free Galerkin implementation of gradient plasticity. Part I: formulation and application to 1D strain localization J. Mech. Beh. Mater. 14 2003 199 231
41. I. Tsagrakis, and E.C. Aifantis Element-free Galerkin implementation of gradient plasticity. Part II: application to 2D strain localization and size effects J. Mech. Beh. Mater. 14 2003 233 270
42. I. Tsagrakis, A. Konstantinidis, and E.C. Aifantis Strain gradient and wavelet interpretation of size effects in yield and strength Mech. Mater. 35 2003 733 745
43. I. Vardoulakis, and E.C. Aifantis A gradient flow theory of plasticity for granular materials Acta Mech. 87 1991 197 217
44. H.M. Zbib, and E.C. Aifantis On the structure and width of shear bands Scr. Met. 22 1988 703 708
45. H.M. Zbib, and E.C. Aifantis A gradient-dependent flow theory of plasticity: application to metal and soil instabilities Appl. Mech. Rev. 42 1989 295 304
46. H.M. Zbib, and E.C. Aifantis On the gradient-dependent theory of plasticity and shear banding Acta Mech. 92 1992 209 225
47. Zhao, J.D., 2002. Localization failure study of geomaterials by strain-gradient-enhanced damage models. Ph.D. dissertation. Tsinghua University, Beijing, China
48. W.Y. Zhou, J.D. Zhao, Y.G. Liu, and Q. Yang Simulation of localization failure with strain-gradient-enhanced damage mechanics Int. J. Numer. Anal. Meth. Geomech. 26 2002 793 813