- Bigoni, Davide and Hueckel, Tomasz, On uniqueness and strain localization in plane strain and plane stress elastoplasticity,
Mechanics Research Communications, vol. 17 no. 1
pp. 15 - 23 [0093-6413(90)90026-9] .
(last updated on 2007/04/09)
The interest in non-uniqueness of the rate problem in small strain elastoplasticity has been renewed by recent attempts to numerically simulate failure in brittle materials such as concrete, rock and soil. In this paper associative plasticity with smooth yield surface allowing for hardening and/or softening is addressed under the assumption of small displacement gradients. Moreover, the restriction is imposed on current stress magnitude which is required to be significantly less than the current elasticity modulus. The latter restriction is usually satisfied in moderately brittle materials, in which the elasticity does not drop significantly due to damage. By specializing the known criterion for localization  to the conditions of plane strain and plane stress, explicit expressions for the critical hardening modulus for localization and for the inclination of the band are found.