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Entropy 2011, 13(11), 1904-1915; doi:10.3390/e13111904

Generalized Hamilton’s Principle for Inelastic Bodies Within Non-Equilibrium Thermodynamics

*  and
State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China
* Author to whom correspondence should be addressed.
Received: 5 September 2011 / Revised: 20 October 2011 / Accepted: 25 October 2011 / Published: 26 October 2011
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Within the thermodynamic framework with internal variables, the classical Hamilton’s principle for elastic bodies is extended to inelastic bodies composed of materials whose free energy densities are point functions of internal variables, or the so‑termed Green-inelastic bodies, subject to finite deformation and non-conservative external forces. Yet this general result holds true even without the Green-inelasticity presumption under a more general interpretation of the infinitesimal internal rearrangement. Three special cases are discussed following the generalized form: (a) the Green-elastic bodies whose free energy can be identified with the strain energy; (b) the Green-inelastic bodies composed of materials compliant with the additive decomposition of strain; and (c) the Green-inelastic bodies undergoing isothermal relaxation processes where the thermodynamic forces conjugate to internal variables, or the so-termed internal forces prove to be potential forces. This paper can be viewed as an extension of Yang et al. [1].
Keywords: Hamilton’s principle; inelastic body; internal variable; internal force Hamilton’s principle; inelastic body; internal variable; internal force
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Leng, K.-D.; Yang, Q. Generalized Hamilton’s Principle for Inelastic Bodies Within Non-Equilibrium Thermodynamics. Entropy 2011, 13, 1904-1915.

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