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Thermodynamics of Infinitesimally Constrained Equilibrium States

[+] Author and Article Information
Q. Yang1

State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, P. R. Chinayangq@tsinghua.edu.cn

L. J. Xue, Y. R. Liu

State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, P. R. China

In this paper, Einstein’s summation convention is adopted for repeated indices. However, if an index range is listed like α in Eq. 15, the index is considered as a free index without the summation convention.

1

Corresponding author.

J. Appl. Mech 76(1), 014502 (Oct 23, 2008) (5 pages) doi:10.1115/1.2998484 History: Received July 02, 2007; Revised September 15, 2008; Published October 23, 2008

This paper is concerned with infinitesimally constrained equilibrium states, which are nonequilibrium states and infinitesimally close to equilibrium states. The corresponding thermodynamics is established in this paper within the thermodynamic framework of Rice (1971, “Inelastic Constitutive Relations for Solids: An Internal Variable Theory and Its Application to Metal Plasticity  ,” J. Mech. Phys. Solids, 19, pp. 433–455). It is shown that the thermodynamics of infinitesimally constrained equilibrium states belongs to linear irreversible thermodynamics. The coefficient matrix is the Hessian matrix of the flow potential function at the equilibrium state. The process of a state change induced by an infinitesimal stress increment in time-independent plasticity can be viewed as a sequence of infinitesimally constrained equilibrium states. The thermodynamic counterpart of yield functions are flow potential functions, and their convexity is required by intrinsic dissipation inequality. Drucker and Il’yushin’s inequalities are not essential thermodynamic requirements.

Copyright © 2009 by American Society of Mechanical Engineers
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