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.
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January 2009
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Thermodynamics of Infinitesimally Constrained Equilibrium States
Q. Yang,
Q. Yang
State Key Laboratory of Hydroscience and Engineering,
e-mail: yangq@tsinghua.edu.cn
Tsinghua University
, Beijing 100084, P. R. China
Search for other works by this author on:
L. J. Xue,
L. J. Xue
State Key Laboratory of Hydroscience and Engineering,
Tsinghua University
, Beijing 100084, P. R. China
Search for other works by this author on:
Y. R. Liu
Y. R. Liu
State Key Laboratory of Hydroscience and Engineering,
Tsinghua University
, Beijing 100084, P. R. China
Search for other works by this author on:
Q. Yang
State Key Laboratory of Hydroscience and Engineering,
Tsinghua University
, Beijing 100084, P. R. Chinae-mail: yangq@tsinghua.edu.cn
L. J. Xue
State Key Laboratory of Hydroscience and Engineering,
Tsinghua University
, Beijing 100084, P. R. China
Y. R. Liu
State Key Laboratory of Hydroscience and Engineering,
Tsinghua University
, Beijing 100084, P. R. ChinaJ. Appl. Mech. Jan 2009, 76(1): 014502 (5 pages)
Published Online: October 23, 2008
Article history
Received:
July 2, 2007
Revised:
September 15, 2008
Published:
October 23, 2008
Citation
Yang, Q., Xue, L. J., and Liu, Y. R. (October 23, 2008). "Thermodynamics of Infinitesimally Constrained Equilibrium States." ASME. J. Appl. Mech. January 2009; 76(1): 014502. https://doi.org/10.1115/1.2998484
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