On linear versus nonlinear flow rules in strain localization analysis

Giorgio Borré; Giulio Maier

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1988)

  • Volume: 82, Issue: 3, page 451-459
  • ISSN: 1120-6330

Abstract

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This note contains some remarks on the analysis of bifurcation phenomena, specifically strain localization (onset of a strain rate discontinuity), in small-deformation elastoplasticity. Nonassociative flow rules are allowed for to cover constitutive models frequently adopted for frictional (and softening) materials such as concrete. The conventional derivation of the localization criterion resting on an incrementally linear "comparison material" is critically reviewed and compared to the criterion resulting from "actual" nonlinear plastic flow laws. This communication anticipates, in an abbreviated form, results to be presented elsewhere in an extended form: therefore proofs of the propositions and various comments are omitted.

How to cite

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Borré, Giorgio, and Maier, Giulio. "On linear versus nonlinear flow rules in strain localization analysis." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 82.3 (1988): 451-459. <http://eudml.org/doc/287240>.

@article{Borré1988,
abstract = {This note contains some remarks on the analysis of bifurcation phenomena, specifically strain localization (onset of a strain rate discontinuity), in small-deformation elastoplasticity. Nonassociative flow rules are allowed for to cover constitutive models frequently adopted for frictional (and softening) materials such as concrete. The conventional derivation of the localization criterion resting on an incrementally linear "comparison material" is critically reviewed and compared to the criterion resulting from "actual" nonlinear plastic flow laws. This communication anticipates, in an abbreviated form, results to be presented elsewhere in an extended form: therefore proofs of the propositions and various comments are omitted.},
author = {Borré, Giorgio, Maier, Giulio},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Plasticity; Localization; Softening; bifurcation; strain rate discontinuity; small-deformation elastoplaticity; Nonassociative flow rules; concrete},
language = {eng},
month = {9},
number = {3},
pages = {451-459},
publisher = {Accademia Nazionale dei Lincei},
title = {On linear versus nonlinear flow rules in strain localization analysis},
url = {http://eudml.org/doc/287240},
volume = {82},
year = {1988},
}

TY - JOUR
AU - Borré, Giorgio
AU - Maier, Giulio
TI - On linear versus nonlinear flow rules in strain localization analysis
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1988/9//
PB - Accademia Nazionale dei Lincei
VL - 82
IS - 3
SP - 451
EP - 459
AB - This note contains some remarks on the analysis of bifurcation phenomena, specifically strain localization (onset of a strain rate discontinuity), in small-deformation elastoplasticity. Nonassociative flow rules are allowed for to cover constitutive models frequently adopted for frictional (and softening) materials such as concrete. The conventional derivation of the localization criterion resting on an incrementally linear "comparison material" is critically reviewed and compared to the criterion resulting from "actual" nonlinear plastic flow laws. This communication anticipates, in an abbreviated form, results to be presented elsewhere in an extended form: therefore proofs of the propositions and various comments are omitted.
LA - eng
KW - Plasticity; Localization; Softening; bifurcation; strain rate discontinuity; small-deformation elastoplaticity; Nonassociative flow rules; concrete
UR - http://eudml.org/doc/287240
ER -

References

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  11. NEEDLEMAN, A. and TVERGAARD, V., «On the Finite Element Analysis of Localization in Plasticity», in: J.T. Oden and G.F. Carey, Eds., Finite Elements-Special Problems in Solid Mechanics5, Prentice-Hall, Englewood Cliffs, N.J., 1983, pp. 94-157. 
  12. ORTIZ, M., LEROY, Y. and NEEDLEMAN, A., «A Finite Element Method for Localized Failure Analysis», Computer Meth. in Appl. Mech. and Eng., Vol. 61, 1987, pp. 189-214. Zbl0597.73105
  13. ORTIZ, M., «An Analytical Study of the Localized Failure Modes of Concrete», Mech. Mat. (to appear). 
  14. PRÉVOST, J.H., «Localization of Deformations in Elastic-Plastic Solids», Internat. J. Numer. Analyt. Meths. Geomech.8, 1984, pp. 187-196. Zbl0532.73071
  15. RANIECKI, B. and BRUHNS, O.T., «Bounds to Bifurcation Stresses in Solids with Non-Associated Plastic Flow Laws at Finite Strain», J. Mech. Phys. Solids, Vol. 29, 1981, pp. 153-172. Zbl0462.73027MR613768DOI10.1016/0022-5096(81)90021-1
  16. RICE, J.R., «The Localization of Plastic Deformation», in: W.T. Koiter, Ed., Theoretical and Applied Mechanics, North-Holland, 1976, pp. 207-220. Zbl0368.73036
  17. RICE, J.R. and RUDNICKI, J.W., «A Note on Some Features of the Theory of Localization of Deformation», Int. J. Solids & Struct., Vol. 16, 1980, pp. 597-605. Zbl0433.73032MR574491
  18. RUDNICKI, J.W. and RICE, J.R., «Conditions for the Localization of Deformation in Pressure-Sensitive Dilatant Materials», J. Mech. Phys. Solids., Vol. 23, 1975, pp. 371-394. 
  19. TVERGAARD, V., NEEDLEMAN, A. and LO, K.K., «Flow Localization in the Plane Strain Tensile Test», J. Mech. Phys. Solids, Vol. 29, 1981, pp. 115-142. Zbl0462.73082
  20. WILLAM, K.J., BICANIC, N. and STURE, S., Constitutive and Computational Aspects of Strain-Softening and Localization in Solids, presented at ASME - WAM '84 Symp. on «Constitutive Equations: Micro, Macro and Computational Aspects», New Orleans, Dec. 1984. 

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