Comparison of the Rudnicki-Rice and Vermeer Bifurcation Criteria

Abstract

Strain localization refers to the formation of narrow zones of intense deformation in materials as a result of bifurcation in the stress-strain response during loading. Bifurcation occurs before the theoretical peak strength is reached and is then followed by strain softening. Theories and criteria have been developed to predict the point of this bifurcation in stress-strain relations. Two bifurcation criteria have been proposed for geomaterials: the complex Rudnicki-Rice criterion and the simple Vermeer criterion. The Rudnicki-Rice criterion is for strain-controlled loading, whereas the Vermeer criterion is for stress-controlled loading. This paper reviews and presents a rigorous and theoretical comparison of the two bifurcation criteria in the context of the flow theory of strain hardening elastoplasticity and shows that the simple Vermeer’s criterion is equivalent to the more complicated Rudnicki-Rice criterion for two-dimensional (2D) loading conditions. However, important differences between the two criteria exist for three-dimensional (3D) loading conditions. This paper also shows that the Rudnicki-Rice criterion provides a more realistic prediction of strain localization in geomaterials during 3D loading than does the Vermeer criterion. The paper is envisioned to offer an improved understanding of strain localization in geomaterials.