The role of deviatone and volumetrie non-associativities on strain localization

Ahmed Benallal; Claudia Comi

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1993)

  • Volume: 4, Issue: 4, page 279-290
  • ISSN: 1120-6330

Abstract

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A homogeneous solid subject to quasi-static loading in the small strain range is considered. The material model assumed is rate-independent, non-associative and incrementally bilinear. The strain localization conditions are analytically solved using a geometric method. The expressions of the critical hardening moduli, their domains of validity and the form of the strain rate discontinuity are obtained. Finally these results, and in particular the role of hydrostatic and deviatoric non-normality, are discussed with reference to an elastic-plastic model for rock-like materials.

How to cite

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Benallal, Ahmed, and Comi, Claudia. "The role of deviatone and volumetrie non-associativities on strain localization." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 4.4 (1993): 279-290. <http://eudml.org/doc/244267>.

@article{Benallal1993,
abstract = {A homogeneous solid subject to quasi-static loading in the small strain range is considered. The material model assumed is rate-independent, non-associative and incrementally bilinear. The strain localization conditions are analytically solved using a geometric method. The expressions of the critical hardening moduli, their domains of validity and the form of the strain rate discontinuity are obtained. Finally these results, and in particular the role of hydrostatic and deviatoric non-normality, are discussed with reference to an elastic-plastic model for rock-like materials.},
author = {Benallal, Ahmed, Comi, Claudia},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Localization; Strain discontinuity; Non-associative plasticity; strain discontinuity; non-associative plasticity; quasi-static loading; geometric method; critical hardening moduli},
language = {eng},
month = {12},
number = {4},
pages = {279-290},
publisher = {Accademia Nazionale dei Lincei},
title = {The role of deviatone and volumetrie non-associativities on strain localization},
url = {http://eudml.org/doc/244267},
volume = {4},
year = {1993},
}

TY - JOUR
AU - Benallal, Ahmed
AU - Comi, Claudia
TI - The role of deviatone and volumetrie non-associativities on strain localization
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1993/12//
PB - Accademia Nazionale dei Lincei
VL - 4
IS - 4
SP - 279
EP - 290
AB - A homogeneous solid subject to quasi-static loading in the small strain range is considered. The material model assumed is rate-independent, non-associative and incrementally bilinear. The strain localization conditions are analytically solved using a geometric method. The expressions of the critical hardening moduli, their domains of validity and the form of the strain rate discontinuity are obtained. Finally these results, and in particular the role of hydrostatic and deviatoric non-normality, are discussed with reference to an elastic-plastic model for rock-like materials.
LA - eng
KW - Localization; Strain discontinuity; Non-associative plasticity; strain discontinuity; non-associative plasticity; quasi-static loading; geometric method; critical hardening moduli
UR - http://eudml.org/doc/244267
ER -

References

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  1. RUDNICKI, J. W. - RICE, J. R., Conditions for the localization of deformation in pressure-sensitive dilatant materials. J. Mech. Phys. Solids, vol. 23, 1975, 371-394. 
  2. RICE, J. R. - RUDNICKI, J. W., A note on some features of the theory of localization of deformation. Int. J. Solids Structures, vol. 16, 1980, 597-605. Zbl0433.73032MR574491
  3. BORRE, G. - MAIER, G., On linear vs. non-linear flow rules in strain localization analysis. Meccanica, vol. 24, 1989, 36-41. Zbl0673.73023MR1013513DOI10.1007/BF01576001
  4. PERRIN, G. - LEBLOND, J. B., Rudnicki and Rice's analysis of strain localization rivisited. J. Appl. Mech., to appear. Zbl0803.73032
  5. OTTOSEN, N. S. - RUNESSON, K., Discontinuous bifurcations in a non-associated Mohrmaterial. Mech. of Materials, vol. 12, 1991, 255-265. 
  6. BIGONI, D. - HEUCKEL, T., Uniqueness and localization - I. Associative and non-associative elastoplasticity. Int. J. Solids Structures, vol. 28, 1991, 197-213. Zbl0749.73017MR1111553DOI10.1016/0020-7683(91)90205-T
  7. BENALLAL, A., On localization phenomena in thermo-elasto-plasticity. Arch. Mech., vol. 44, 1992, 15-29. Zbl0757.73001
  8. BENALLAL, A. - COMI, C., Explicit solutions to localization conditions via a geometrical method. The coaxial case. Rapport interne, LMT Cachan, février 1993. 
  9. CHEN, W. F. - HAN, D. J., Plasticity for structural engineers. Springer-Verlag, 1987. Zbl0666.73010

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