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

  • Qiang Yang EMAIL logo , Chaoyi Li and Yaoru Liu
Published/Copyright: March 19, 2021

Abstract

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.

Award Identifier / Grant number: 2018YFC0407005

Award Identifier / Grant number: 51739006

Award Identifier / Grant number: 41961134032

Funding statement: This work has been supported by the National Key R&D Program of China (2018YFC0407005) and National Natural Science Foundation of China under projects 51739006 and 41961134032.

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Received: 2020-07-07
Revised: 2021-02-23
Accepted: 2021-03-02
Published Online: 2021-03-19
Published in Print: 2021-07-26

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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