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.

中文翻译：

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由自由能函数的非弹性微分公式化的与时间无关的塑性

作者提出了一种与时间无关的塑性方法，其中典型的塑性加载过程被视为两个相邻平衡状态的无穷小状态变化，并且屈服和一致性条件是基于内部变量的共轭力制定的。在本文中，提出了一个稳定条件，并通过吉布斯自由能的非弹性微分形式重新格式化了屈服、一致性和稳定条件。具有内部变量的热力学中的吉布斯方程是通过单个吉布斯自由能函数对吉布斯自由能的微分形式的表示。在本文中，我们提出了所谓的扩展吉布斯方程，其中微分形式可以由多个势函数表示。具有单个或多个屈服函数的各种关联和非关联塑性可以从基于重构方法的各种表示中导出，其中屈服和塑性势函数采用势函数的非弹性微分形式。广义德鲁克不等式只能从作为稳定条件的单势表示导出。对于多势能表示，如果多势是凹函数且具有相同的驻点，则可以保证稳定条件。广义德鲁克不等式只能从作为稳定条件的单势表示导出。对于多势能表示，如果多势是凹函数且具有相同的驻点，则可以保证稳定条件。广义德鲁克不等式只能从作为稳定条件的单势表示导出。对于多势能表示，如果多势是凹函数且具有相同的驻点，则可以保证稳定条件。