Evaluation of Plastic Bifurcation for Plane Strain versus Axisymmetry

Abstract

Properties of discontinuous bifurcation solutions for elastic‐plastic solids are established for conventional test conditions that are pertinent to experiments on soil, powder, and rock. Typically, such conditions are characterized as plane strain and axisymmetry. A restricted form of nonassociativity is assumed, where only the volumetric portion of the flow rule is nonassociated. Apart from this restriction, the aim is to make as general predictions as possible without resorting to a specific elastic‐plastic model. It is shown that states of plane strain are far more susceptible to bifurcations than those encountered in the conventional triaxial apparatus (which represents cylindrical stress states). Moreover, the solutions for dilatant materials will rarely bifurcate under conventional triaxial compression (CTC) test conditions, while conventional triaxial extension (CTE) test conditions fall between the two extremes of plane strain and CTC. For Drucker‐Prager criterion it is shown that bifurcation is never possible in the hardening regime for CTC. These findings are in agreement with experimentally observed behavior when it can be ensured that the stress state is sufficiently homogeneous throughout the specimen.