Discontinuous bifurcations in a nonassociated Mohr material

Discontinuous bifurcations of an elastic-plastic material obeying Mohr's yield criterion and a nonassociated flow rule and subjected to general three-dimensional loading are investigated. The first possibility for bifurcation is identified and expressed in terms of the critical hardening modulus and the corresponding orientation of the slip planes. In the case of perfect plasticity the Mohr and Roscoe solutions for the orientation of the slip planes are derived. The corresponding strain rate fields are determined and it is shown that the Roscoe strain rate field differs significantly from the other fields. Moreover, the stress rate field is continuous across the singular surface for the Roscoe solution.