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Properties of Discontinuous Bifurcations Solutions in Elasto-Plasticity

Ottosen, Niels Saabye LU and Runesson, Kenneth (1991) In International Journal of Solids and Structures 27(4). p.401-421
Abstract
Explicit expressions for the spectral properties of the bifurcation problem involving discontinuities for general elastic-plastic materials are presented. It then follows that the classical value of the critical hardening modulus derived by Rice (1976. Proc. 14th IUTAM Congr., Delft, The Netherlands, pp. 207–220, North Holland, Amsterdam.) is, in fact, the only possible one. Furthermore, from the spectral analysis it follows in a very straightforward fashion that bifurcation displaying elastic unloading on one side of the singular surface can never precede bifurcation with plastic loading on both sides of this surface. Explicit analytical results for the critical bifurcation directions and the corresponding hardening modulus are derived... (More)
Explicit expressions for the spectral properties of the bifurcation problem involving discontinuities for general elastic-plastic materials are presented. It then follows that the classical value of the critical hardening modulus derived by Rice (1976. Proc. 14th IUTAM Congr., Delft, The Netherlands, pp. 207–220, North Holland, Amsterdam.) is, in fact, the only possible one. Furthermore, from the spectral analysis it follows in a very straightforward fashion that bifurcation displaying elastic unloading on one side of the singular surface can never precede bifurcation with plastic loading on both sides of this surface. Explicit analytical results for the critical bifurcation directions and the corresponding hardening modulus are derived for non-associated volumetric flow rules while the devialoric portion is associated. The considered yield and potential functions may depend on all three stress invariants and may involve mixed isotropic and kinematic hardening. The result obtained by Rudnicki and Rice (1975, J. Mech. Phys. Solids 23, 371–394) for a Drucker-Pruger material appear as a special case. Other criteria that are investigated arc those of Coulomb and Rankine. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
International Journal of Solids and Structures
volume
27
issue
4
pages
401 - 421
publisher
Elsevier
external identifiers
  • Scopus:0025852818
ISSN
0020-7683
DOI
10.1016/0020-7683(91)90131-X
language
English
LU publication?
yes
id
8b70aeeb-b9cc-4211-997e-44ccad668c46 (old id 1370101)
date added to LUP
2010-08-24 16:21:57
date last changed
2016-11-06 04:31:14
@misc{8b70aeeb-b9cc-4211-997e-44ccad668c46,
  abstract     = {Explicit expressions for the spectral properties of the bifurcation problem involving discontinuities for general elastic-plastic materials are presented. It then follows that the classical value of the critical hardening modulus derived by Rice (1976. Proc. 14th IUTAM Congr., Delft, The Netherlands, pp. 207–220, North Holland, Amsterdam.) is, in fact, the only possible one. Furthermore, from the spectral analysis it follows in a very straightforward fashion that bifurcation displaying elastic unloading on one side of the singular surface can never precede bifurcation with plastic loading on both sides of this surface. Explicit analytical results for the critical bifurcation directions and the corresponding hardening modulus are derived for non-associated volumetric flow rules while the devialoric portion is associated. The considered yield and potential functions may depend on all three stress invariants and may involve mixed isotropic and kinematic hardening. The result obtained by Rudnicki and Rice (1975, J. Mech. Phys. Solids 23, 371–394) for a Drucker-Pruger material appear as a special case. Other criteria that are investigated arc those of Coulomb and Rankine.},
  author       = {Ottosen, Niels Saabye and Runesson, Kenneth},
  issn         = {0020-7683},
  language     = {eng},
  number       = {4},
  pages        = {401--421},
  publisher    = {ARRAY(0xc07d348)},
  series       = {International Journal of Solids and Structures},
  title        = {Properties of Discontinuous Bifurcations Solutions in Elasto-Plasticity},
  url          = {http://dx.doi.org/10.1016/0020-7683(91)90131-X},
  volume       = {27},
  year         = {1991},
}