Derivation of transformed stress method based on indirect thermodynamic method

The unique plastic potential function consistent with the yield function can be directly determined by the Drucker's postulate and its associated flow law deduction after the yield function is established for the continuous materials without dilatancy, such as metals. However, a large number of test results and theoretical analyses show that the Drucker's postulate is not applicable to soils, which is a type of granular material with dilatancy, then the more universal thermodynamics is selected as a new necessary condition for correctly describing the plastic flow direction of soils. Nevertheless, the plastic flow direction cannot be determined solely by thermodynamics, which is only a necessary condition to describe the properties of materials. Therefore, the indirect thermodynamic method is developed in which the yield surface and the plastic flow direction are firstly determined with tests and then verified by thermodynamics. In addition, since the stress-strain relationships on the meridional planes corresponding to different Lode angles in the three-dimensional stress space of soils are not consistent to each other, the generalized methods are generally used to describe such mechanical characteristics of soils. Meanwhile, the generalized yield surface and plastic flow direction on different meridional planes will be different from those in the constitutive models established under triaxial compression state, so whether the generalized constitutive model conforms to the thermodynamics becomes a new problem. Therefore, the indirect thermodynamic method is used to derive a generalized method conforming to the principles of thermodynamics, which is then organized into a more practical transformed stress method by constructing the transformation stress space.