A boundary element technique for incremental, non-linear elasticity Part II: Bifurcation and shear bands

Computer Methods in Applied Mechanics and Engineering

Volumn 192, Issue 22-23, 2003, Pages 2481-2499

  Brun, M ^a   Bigoni, D ^a   Capuani, D ^b  

^a UNIVERSITY OF TRENTO   (Italy)

^b UNIVERSITY OF FERRARA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); BOUNDARY ELEMENT METHOD; ELASTICITY; MULTILAYERS; PERTURBATION TECHNIQUES;

ELASTIC DEFORMATIONS;

DEFORMATION;

BIFURCATION; BOUNDARY ELEMENT METHOD; DEFORMATION; ELASTICITY; STRAIN ANALYSIS;

EID: 0037671236     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(03)00272-X     Document Type: Article

References (57)

1. Aliabadi M.H. Boundary element formulations in fracture mechanics Appl. Mech. Rev. 50 1997 83-96
2. Armero F. On the characterization of localized solutions in inelastic solids: an analysis of wave propagation in a softening bar Comput. Methods Appl. Mech. Engrg. 191 2001 181-213
3. Armero F. Garikipati K. An analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids Int. J. Solids Struct. 33 1996 2863-2885
4. Bardet J.P. Finite-element analysis of surface instability in hypoelastic solids Comput. Methods Appl. Mech. Engrg. 78 1990 273-296
5. Bazant Z.P. Belytschko M. Chang T.P. Continuum theory for strain-softening ASCE J. Engrg. Mech. 110 1984 1666-1691
6. Belytschko T. Fish J. Englemann B. A finite element with embedded localization zones Comput. Methods Appl. Mech. Engrg. 70 1988 59-89
7. Benallal A. Billardon R. Geymonat G. Some mathematical aspects of the damage softening problem Mazar J. Bazant Z.P. Cracking and Damage vol. 1 1988 247-258
8. Benallal A. Billardon R. Geymonat G. Bifurcation and localization in rate-independent materials: some general considerations CISM Lecture Notes No. 327 1993 1-47 Springer Berlin
9. Benallal A. Fudoli C.A. Venturing W.S. An implicit BEM formulation for gradient plasticity and localization phenomena Int. J. Numer. Methods Engrg. 53 2002 1853-1869
10. Bigoni D. Bifurcation and instability of non-associative elastoplastic solids Petryk H. Material Instabilities in Elastic and Plastic Solids CISM Lecture Notes No. 414 2000 1-52 Springer Berlin
11. Bigoni D. Capuani D. Green's function for incremental nonlinear elasticity: shear bands and boundary integral formulation J. Mech. Phys. Solids 50 2002 471-500
12. D. Bigoni, M. Gei, On bifurcation of a layered, orthotropic, elastic medium, XXVIII AIAS National Congress, Vicenza, Italy, 8-11 September 1999
13. Bigoni D. Ortiz M. Needleman A. Effect of interfacial compliance on bifurcation of a layer bonded to a substrate Int. J. Solids Struct. 34 1997 4305-4326
14. Biot M.A. Mechanics of Incremental Deformations 1965 John Wiley and Sons New York
15. Borja R.I. Finite element simulation of strain localization with large deformation: capturing strong discontinuity using a Petrov-Galerkin multiscale formulation Comput. Methods Appl. Mech. Engrg. 191 2002 2949-2978
16. de Borst R. Sluys L.J. Localization in a Cosserat continuum under static and dynamic loading conditions Comput. Methods Appl. Mech. Engrg. 90 1991 805-827
17. Coleman B.D. Hodgon M.L. On shear bands in ductile materials Arch. Rat Mech. Anal. 90 1985 219-247
18. Cruse T.A. Boundary Element Analysis in Computational Fracture Mechanics 1988 Kluwer Academic Press Dodrecht
19. D'Ambrosio P. De Tommasi D. Marzano S. Nonlinear elastic deformations and stability of laminated rubber bearings ASCE J. Engrg. Mech. 121 1995 1041-1048
20. Deb A. Prevost J.H. Loret B. Adaptive meshing for dynamic strain localization Comput. Methods Appl. Mech. Engrg. 137 1996 285-306
21. Deb A. Loret B. Prevost J.H. Automated band identification procedure for dynamic strain localization Comput. Methods Appl. Mech. Engrg. 137 1996 307-330
22. Desrues J. Chambon R. Shear band analysis and shear moduli calibration Int. J. Solids Struct. 39 2002 3757-3776
23. Fleck N.A. Hutchinson J.W. A phenomenological theory for strain gradient effects in plasticity J. Mech. Phys. Solids 41 1993 1825-1857
24. Fleck N.A. Hutchinson J.W. Strain gradient plasticity Advances in Applied Mechanics vol. 33 1997 295-361 Academic Press New York
25. Hill R. Hutchinson J.W. Bifurcation phenomena in the plane tension test J. Mech. Phys. Solids 23 1975 239-264
26. Huiskes R. Ruimerman R. van Lenthe G.H. Janssen J.D. Effects of mechanical forces on maintenance and adaptation of form in trabecular bone Nature 405 2000 704-706
27. Hutchinson J.W. Tvergaard V. Surface instabilities on statically strained plastic solids Int. J. Mech. Sci. 22 1980 339-354
28. Lizuka M. A macroscopic model for predicting large-deformation behaviors of laminated rubber bearings Engrg. Struct. 22 2000 323-334
29. Imbimbo M. De Luca A. F.E. stress analysis of rubber bearing under axial loads Comput. Struct. 68 1998 31-39
30. Imbimbo M. Kelly J.M. Influence of material stiffening on stability of elastomeric bearings at large displacements ASCE J. Engrg. Mech. 124 1998 1045-1049
31. Kelly J.M. Earthquake-resistant Design with Rubber 1997 Springer-Verlag Berlin
32. Larsson R. Runesson K. Ottosen N.S. Discontinuous displacement approximation for capturing plastic localization Int. J. Numer. Methods Engrg. 36 1993 2087-2105
33. Leblond J.B. Perrin G. Devaux J. Bifurcation effects in ductile metals with nonlocal damage J. Appl. Mech. 61 1994 236-242
34. Loret B. Prevost J.H. Dynamic strain localization in elasto-(visco-)plastic solids. Part 1: General formulation and one-dimensional examples Comput. Methods Appl. Mech. Engrg. 83 1990 247-273
35. Mühlhaus H.B. Vardoulakis I. The thickness of shear bands in granular materials Geotechnique 37 1987 271-283
36. Menzel A. Steinmann P. On the continuum formulation of higher gradient plasticity for single and polycrystals J. Mech. Phys. Solids 48 2000 1777-1796
37. Nacar A. Needleman A. Ortiz M. A finite element method for analyzing localization in rate dependent solids at finite strains Comput. Methods Appl. Mech. Engrg. 73 1989 235-258
38. Needleman A. Material rate dependence and mesh sensitivity in localization problems Comput. Methods Appl. Mech. Engrg. 67 1988 69-85
39. Oliver J. On the discrete constitutive models induced by strong discontinuity kinematics and continuum constitutive equations Int. J. Solids Struct. 37 2000 7207-7229
40. H. Petryk, On energy criteria of plastic instability, in: Plastic Instability, Proc. Considére Memorial. Ecole Nat. Fonts Chauss., Paris, 1985, pp. 215-226
41. Petryk H. Thermann K. Post-critical plastic deformation of biaxially stretched sheets Int. J. Solids Struct. 33 1996 689-705
42. Petryk H. Thermann K. Post-critical plastic deformation in incrementally nonlinear materials J. Mech. Phys. Solids 50 2002 925-954
43. Pietruszczak S. Mróz Z. Finite element analysis of deformation of strain-softening materials Int. J. Numer. Methods Engrg. 17 1981 327-334
44. Pijaudier-Cabot G. Bazant Z.P. Nonlocal damage theory ASCE J. Engrg. Mech. 113 1987 1512-1533
45. Radi E. Bigoni D. Capuani D. Effects of pre-stress on crack-tip fields in elastic, incompressible solids Int. J. Solids Struct. 39 2002 3971-3996
46. Ryzhak E.I. On stable deformation of "unstable" materials in a rigid triaxial testing machine J. Mech. Phys. Solids 41 1993 1345-1356
47. Ryzhak E.I. On stability of homogeneous elastic bodies under boundary-conditions weaker than displacement conditions Quart. J. Mech. Appl. Math. 47 1994 663-672
48. Ryzhak E.I. A case of indispensable localized instability in elastic-plastic solids Int. J. Solids Struct. 36 1999 4669-4691
49. Simo J.C. Oliver J. Armero F. An analysis of strong discontinuities induced by softening solutions in rate-independent solids J. Comput. Mech. 12 1993 277-296
50. Sluys L.J. Estrin Y. The analysis of shear banding with a dislocation based gradient plasticity model Int. J. Solids Struct. 37 2000 7127-7142
51. Stanton J.F. Scroggins G. Taylor A.W. Roeder C.W. Stability of aminated elastomeric bearings ASCE J. Engrg. Mech. 116 1990 1351-1371
52. Triantafyllidis N. Aifantis E. A gradient approach to localization of deformation: I. Hyperelastic materials J. Elast. 16 1986 225-237
53. Tsai H.-C. Hsueh S.-J. Mechanical properties of isolation bearings identified by a viscoelastic model Int. J. Solids Struct. 38 2001 53-74
54. Tvergaard V. Influence of void nucleation on ductile shear fracture at a free surface J. Mech. Phys. Solids 30 1982 399-425
55. L. van Hove, Sur l'extension de la condition de Legendre du calcul des variations aux intégrales multiples à plusieurs fonctions inconnues, Proc. Sect. Sci. K. Akad. van Wetenschappen, Amsterdam, vol. 50, 1947, pp. 18-23
56. Vardoulakis I. Afantis E. A gradient flow theory of plasticity for granular materials Acta Mech. 87 1991 197-217
57. Young N.B.J. Bifurcation phenomena in the plane compression test J. Mech. Phys. Solids 24 1976 77-91