Flow rules for rigid-plastic strain kinematic hardening solids

•It is shown that the associated flow rule is not valid in rigid-plastic deformations.•The associated flow rule for von Mises materials exhibiting kinematic hardening is modified.•The principle of the maximum plastic dissipation is modified.

The associated flow rule is commonly supposed to be one of the cornerstones of classical plasticity theory for metals though some experimental results do not accord with it. This paper investigates the flow rule of plastic deformation rate for von Mises materials exhibiting kinematic hardening. It is found that the associated flow rule is not valid in rigid-plastic deformations. The associated flow rule for von Mises materials exhibiting kinematic hardening is modified. The modified associated flow rule implies that the vector of plastic deformation rate need not be perpendicular to the yield surface in nine-dimensional stress space. Finally, the principle of maximum plastic dissipation is modified as well.