A class of phenomenological corner theories of plasticity

A class of phenomenological flow theories of plasticity is proposed which models time-independent incremental behavior at a corner of the yield surface of a polycrystalline metal. The proposal is consistent with the physical theories of plasticity based on single crystal slip. Conditions for convexity, ensuring invertibility of the incremental relations, are derived. The simplest candidate, called J2 corner theory, coincides with the J2 deformation theory of plasticity for nearly proportional stress increments and incorporates a smooth transition to elastic unloading for increasingly non-proportional increments. The theory is applied to the bifurcation and imperfection-sensitivity analysis of necking in a thin sheet. For this example, like many others involving bifurcation in the plastic range, the corner theory appears to circumvent some of the difficulties associated with use of the standard phenomenological plasticity laws.