Piecewise Linear Yield Criteria in Invariant Form

Abstract

General piecewise-linear yield criteria exhibiting 30°, 60°, or 120° symmetry in the octahedral plane are expressed in terms of the canonical invariants of the deviator stress, J\d2 and J\d3. Criteria of the type often associated with granular media, in which strength is proportional to the hydrostatic component of stress, are also reviewed. In the particular case of the Coulomb criterion, it is shown that compact expressions can be found through the use of the canonical invariants of stress I\d1, I\d2, and I\d3.