Mechanism of non-associated flow rule based on Hill's principle

nth homogeneous yield criteria related to friction effect is independent of true stress in classical plasticity and even equal to zero for sand materials. The latter does not conform to the second law of thermodynamics, which demonstrates that the dissipative work must be bigger than zero during the appearance of plastic behavior. Hill's principle of maximum dissipative work was generalized from true stress space to dissipative stress space. According to the mechanism that the energy dissipation resulted from friction is related to normal stress (or spherical stress) of true stress, a partial function related to true stress was added into the yield function of dissipative space in order that the dissipative work is bigger than zero during the appearance of plastic behavior. Because the yield criterion of dissipative space was relative to the true stress, the relation between the yield criteria of true space and plastic strain conformed to non-associated flow rule.