Failure mechanism of associated flow rule for nth homogenous yield function

Some commonly-used classical yield criteria related to friction effect in geomaterials belong to nth Euler homogeneous function. Such criteria refer to Mohr-Coulomb yield criterion, generalized Yu Maohong twin shear stress yield criterion, Lade-Duncan yield criterion, Matsuoka-Nakai yield criterion and Shen Zhujiang three-shear stress yield criterion. After this type of yield criteria is extended from true space to dissipative space, it is found that if nth homogeneous yield criterion in dissipative space is independent of true stress, the dissipative work based on the Drucker's plastic postulate in dissipative space will be independent of stress state, and even equal to zero for sand materials, the latter of which does not conform to the second law of thermodynamics which demonstrates that entropy production must be larger than zero during the appearance of plastic behavior. To avoid this unconformity, a partial function related to the true stress must be added into the nth homogeneous yield function in dissipative space. Therefore, the relation between the new obtained yield criterion in true space and the increment of plastic strain must conform to the non-associated flow rule. Because the expression of the yield criteria in dissipative space is the same as that in true space on the condition of the associated flow rule, the associated flow rule is invalid for geomaterials with friction effect and nth homogeneous yield criteria in true space.