Variational multiscale approach to strain localization - formulation for multidimensional problems

Computer Methods in Applied Mechanics and Engineering

Volumn 188, Issue 1, 2000, Pages 39-60

  Garikipati, K ^a,b   Hughes, T J R ^a  

^a Stanford University   (United States)

^b STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

INTERPOLATION; PROBLEM SOLVING; SENSITIVITY ANALYSIS; VARIATIONAL TECHNIQUES;

STRAIN LOCALIZATION;

STRAIN;

EID: 0034226528     PISSN: 00457825     EISSN: None     Source Type: None    
DOI: 10.1016/S0045-7825(99)00156-5     Document Type: Article

References (53)

1. T.J.R. Hughes Multiscale phenomena green's functions the Dirichlet-to-Neumann formulation subgrid scale models bubbles and the origins of stabilized ethods Comput. Meth. Appl. Mech. Engrg. 127 1995 387 401
2. T.J.R. Hughes A space–time formulation for multiscale phenomena J. Comput. Appl. Math. 74 1996 217 229
3. K. Garikipati T.J.R. Hughes A study of strain localization in a multiple scale framework – the one-dimensional problem Comput. Meth. Appl. Mech. Engrg. 159 1998 193 222
4. T.Y. Thomas, Plastic Flow and Fracture in Solids, Academic Press, New York, 1961
5. R. Hill Acceleration waves in solids J. Mech. Phys. Solids 10 1962 1 16
6. J. Mandel, Conditions de Stabilité et Postulat de Drucker, in: J. Kravtchenko, P.M. Sirieys (Eds.), Rheology and Soil Mechanics, IUTAM Symposium, 1964, pp. 58–68
7. R. Hill J.W. Hutchinson Bifurcation phenomena in the plane tension test J. Mech. Phys. Solids 23 1975 239 264
8. J.R. Rice, The localization of plastic deformation, in: W.T. Koiter (Ed.), Theoretical and Applied Mechanics, North Holland, Amsterdam, 1976, pp. 207–220
9. R.J. Asaro Micromechanics of crystals and polycrystals Adv. Appl. Mech. 23 1983 1 115
10. C. Truesdell, W. Noll, The Non-linear Field Theories (Handbuch der Physik band III), Springer, Berlin, 1965
11. K.F. Graff, Wave Motion in Elastic Solids, Dover, New York, 1975
12. J.E. Marsden, T.J.R. Hughes, Mathematical Foundations of Elasticity, Dover, New York, 1994
13. J.W. Rudnicki J.R. Rice Conditions for the localization of deformation in pressure-sensitive dilatant materials J. Mech. Phys. Solids 23 1975 371 394
14. J.R. Rice J.W. Rudnicki A note on some features of the theory of localization of deformation Int. J. Solids and Structures 16 1980 597 605
15. K. Willam, Experimental and computational aspects of concrete fracture, in: R. Owen, E. Hinton, Bićanić (Eds.), Proceedings of the International Conference on Computer Aided Analysis and Design of Concrete Structures, Pineridge, Swansea, 1984, pp. 33–70
16. N.S. Ottosen K. Runesson Properties of discontinuous bifurcation solutions in elasto-plasticity Int. J. Solids and Structures 27 1991 401 421
17. D. Bigoni D. Zaccaria On strain localization analysis of elastoplastic materials at finite strains Int. J. Plasticity 9 1993 21 33
18. L. Anand K.H. Kim T.G. Shawki Onset of shear localization in viscoplastic solids J. Mech. Phys. Solids 35 1987 407 429
19. T.G. Shawki R.J. Clifton Shear band formation in thermal viscoplastic materials Machanics of Materials 8 1989 13 43
20. A. Needleman Dynamic shear band development in plane strain J. Appl. Mach. 56 1989 1 9
21. R.C. Batra D.S. Liu Adiabatic shear banding in plane strain problems J. Mech. Phys. Solids 56 1989 527 534
22. J. Hadamard, Leçons sur la Propagation des Ondes et les Equations de l'Hydro-dynamique, Hermann, Paris, 1903
23. H. Geiringer, Beitrag zum Vollständingen Ebenen Plastizitätsproblem, in: Proccedings of the Third International Congress Applied Mechanics, Stockholm, 1930, pp. 185–190
24. H. Matthies, G. Strang, E. Christiansen, The saddle point of a differential program energy methods in finite element analysis, in: R. Glowinski, E.Y. Rodin, O.C. Zienkiewicz (Eds.), Wiley, New York, 1979, pp. 309–318
25. J.C. Simo J. Oliver F. Armero An analysis of strong discontinuities induced by softening solutions in rate-independent solids J. Comput. Mech. 12 1993 277 296
26. J.C. Simo, J. Oliver, A new approach to the analysis and simulation of strain softening in solids, in: Z.P. Bazant, Z. Bittnar, M. Jirásek, J. Mazars (Eds.), Fracture and Damage in Quasibrittle Structures, 1994
27. F. Armero, K. Garikipati, Recent advances in the analysis and numerical simulation of strain localization in inelastic solids, in: D.R.J. Owen, E. Oñate, E. Hinton (Eds.), Proceedings of the Computational Plasticity IV, CIMNE, Barcelona, 1995, pp. 547–561
28. F. Armero K. Garikipati 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 and Structures 33 1996 2863 2885
29. J. Oliver Modelling strong discontinuities in solid mechanics via strain softening constitutive equations. Part 1: Fundamentals Int. J. Numer. Methods Engrg. 39 1996 3575 3600
30. St. Pietruszczak Z. Mróz Finite element analysis of deformation of strain-softening materials Int. J. Numer. Methods Engrg. 17 1981 327 334
31. H.E. Read G.A. Hegemier Strain softening of rock soil and concrete – a review article Mechanics of Materials 3 1984 271 294
32. Z.P. Bazant Mechanics of distributed cracking Appl. Mech. Rev. 39 1986 675 705
33. A. Hillerborg M. Modéer P.E. Petersson Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements Cement and Concrete Res. 6 1976 773 782
34. A. Hillerborg, Numerical methods to simulate softening and fracture of concrete, in: G.C. Sih, A. di Tomasso (Eds.), Fracture Mechanics of Concrete: Structural Application and Numerical Calculation, Martinus Nijhoff, Dordrecht, 1985, pp. 141–170
35. Z.P. Bazant B.H. Oh Crack band theory for fracture of concrete Matèriaux et Constructions 39 1983 155 177
36. Z.P. Bazant T.B. Belytschko T.P. Chang Continuum theory for strain softening J. Engrg. Mech. 110 1984 1666 1691
37. L. Stromberg M. Ristinmaa Finite element formulation of a non-local plasticity theory Comput. Methods in Appl. Mech. Engrg. 136 1996 127 144
38. B.D. Coleman M.L. Hodgdon On shear bands in ductile materials Archives for Rational Mech. Anal. 90 1985 219 247
39. R.H.J. Peerlings R. de Borst A.M. Brekelmans J.H.P. de Vree Gradient enhanced damage for quasi-brittle materials Int. J. Numer. Methods Engrg. 39 1996 3391 3403
40. R. de Borst J. Pamin Some novel developments in finite element procedures for strain gradient-dependent plasticity Int. J. Numer. Methods Engrg. 39 1996 2477 2505
41. R. de Borst L.J. Sluys Localisation in a cosserat continuum under static and dynamic loading conditions Comput. Methods Appl. Mech. Engrg. 90 1991 805 827
42. J. Yu, D. Peric, D.R.J. Owen, An ssessment of the cosserat continuum through the finite element simulation of a strain localisation problem, in: E. Oñate, J. Periaux, A. Samuelsson (Eds.), Springer/CIMNE, Barcelona, 1991, pp. 321–332
43. T.B. Belytschko J. Fish B.E. Engleman A finite element with embedded localization zones Comput. Methods Appl. Mech. Engrg. 70 1988 59 89
44. M. Ortiz Y. Leroy A. Needleman A finite element method for localized failure analysis Comput. Methods Appl. Mech. Engrg. 61 1987 189 214
45. R. Larsson, K. Runesson, M. Akesson, Embedded localization band based on regularized strong discontinuity, in: D.R.J. Owen, E. Oñate, E. Hinton (Eds.), Proceedings of Computational Plasticity IV, CIMNE, Barcelona, 1995, pp. 599–609
46. K. Garikipati, T.J.R. Hughes, A study of strong discontinuities in a multiple scale framework, Int. J. Comput. Civil and Structural Engineering, 1999, to appear in the inaugural issue
47. J.C. Simo M.S. Rifai A class of mixed assumed strain methods and the method of incompatible modes Int. J. Numer. Methods Engrg. 29 1990 1595 1638
48. K. Arunakirinathar B.D. Reddy Further results for enhanced strain methods with isoparametric elements Comput. Methods Appl. Mech. Engrg. 127 1995 127 143
49. F. Brezzi, M. Fortin, Mixed and Hybrid Finite Element Methods Springer, New York, 1991
50. J.C. Simo, T.J.R. Hughes, Computational Inelasticity, Springer, 1998
51. K. Garikipati, On strong discontinuities in inelastic solids and their numerical simulation, Ph.D. Thesis, Stanford University, 1996
52. V. Tvergaard A. Needleman K.K. Lo Flow localization in the plane strain tension test J. Mech. Phys. Solids 29 1981 115 142
53. W.D. Nix H. Gao Indentation size effects in crystalline materials: a law for strain gradient plasticity J. Mech. Phys. Solids 46 1998 411 425