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The authors presented a time-independent plasticity approach, where a typical plastic-loading process is viewed as an infinitesimal state change of two neighboring equilibrium states, and the yield and consistency conditions are formulated based on the conjugate forces of the internal variables. In this paper, a stability condition is proposed, and the yield, consistency, and stability conditions are reformatted by the inelastic differential form of the Gibbs free energy. The Gibbs equation in thermodynamics with internal variables is a representation to the differential form of the Gibbs free energy by a single Gibbs free energy function. In this paper, we propose the so-called extended Gibbs equation, where the differential form may be represented by multiple potential functions. Various associated and nonassociated plasticity with a single or multiple yield functions can be derived from various representations based on the reformulated approach, where yield and plastic potential functions are in the form of inelastic differentials of the potential functions. The generalized Drucker inequality can only be derived from the one-potential representation as a stability condition. For a multiple-potential representation, the stability condition can be ensured if the multiple potentials are concave functions and possess the same stationary point.

Time-Independent Plasticity Formulated by Inelastic Differential of Free Energy Function