DISCONTINUOUS BIFURCATIONS OF ELASTIC PLASTIC SOLUTIONS AT PLANE-STRESS AND PLANE-STRAIN

Conditions for discontinuous bifurcations of the incremental fields in elastic-plastic materials subjected to the condition of either plane stress or plane strain are derived and explicit expressions for the critical hardening modulus and the corresponding bifurcation directions are obtained for a quite general class of plasticity models. The only restriction is that the gradients of the yield function and plastic potential, that defines the nonassociated flow rule, have the same principal directions and that two of these directions are located in the plane of interest. Drucker-Prager's and Mohr-Coulomb's yield criteria are taken as typical for the behavior of pressure-dependent materials such as concrete and granular materials. For the latter criterion, results for plane strain have previously been obtained only for the very particular case when the intermediate principal stress is directed out-of-plane. These results are confirmed in this paper as a part of the investigation of the complete behavior.