The expressions of generalized shear stress and generalized shear strain are introduced. After analyzing the two expressions

mistakes in calculating the increment of generalized shear stress and generalized shear strain are pointed out

and then the right calculations are given. Based on this

two expressions of work increment that one is described by mean stress

volumetric strain increment

generalized shear stress and generalized shear strain increment and the other is described by three-dimensional stresses and three-dimensional strain increments are compared. The conclusion is that the two expressions are not always consistent except in some particular conditions. An example of the particular conditions is that loading in constant Lode angle and also the Lode angle of the three-dimensional stresses is equal to that of the three-dimensional strain increments. The same inconsistency still exists in applications of plastic work increment

while unfortunately the equation of Lode angle of the three-dimensional stresses and the three-dimensional strain increments is not always satisfied for practical geomaterials. So in the theory of geotechnical plasticity

for the condition of loading in constant Lode angle

the plastic work increment expressed by mean stress

plastic volumetric strain increment

generalized shear stress and generalized plastic shear strain increment is just a kind of approximation.