Localized deformations such as shear bands, compaction bands, dilation bands, combined shear/compaction or shear/dilation bands, fractures, and joint slippage are commonly found in geomaterials like soil and rock. Thus, modeling their inception, development, and propagation, and effect on mechanical response of the body or structure is important. The paper will focus on one, now classical, analysis method for modeling the inception of these localized deformations for a rate-sensitive, non-associative, three-invariant, isotropic/kinematic hardening cap plasticity model. Bifurcation analysis, in terms of continuous and discontinuous conditions (Int. J. Solids Struct. 1980; 16:597-605), provides the mathematical conditions under which a localized deformation mode could be admissible, and it should not to be confused with attempting to model the microstructural evolution of the geomaterial as it transitions from a nearly uniform to localized deformation response at a material point. Analysis determines that continuous and discontinuous bifurcation are different for weak discontinuity and the same for strong discontinuity, and such conditions are identified for the plasticity model. Rate sensitivity will preclude bifurcation regardless of viscosity value. Numerical examples demonstrate various plasticity model features that enable detection of localization using bifurcation analysis. All analyses are conducted currently in the small strain regime. Copyright (C) 2010 John Wiley & Sons, Ltd.
