Generalized Hamilton’s Principle for Inelastic Bodies Within Non-Equilibrium Thermodynamics
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 de...
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| Format: | Article |
| Language: | English |
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MDPI AG
2011-10-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/13/11/1904/ |
| _version_ | 1798003489568194560 |
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| author | Qiang Yang Kuang-Dai Leng |
| author_facet | Qiang Yang Kuang-Dai Leng |
| author_sort | Qiang Yang |
| collection | DOAJ |
| description | 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]. |
| first_indexed | 2024-04-11T12:08:25Z |
| format | Article |
| id | doaj.art-5d4f351d37f84aa48c7efe44a855e2ae |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T12:08:25Z |
| publishDate | 2011-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-5d4f351d37f84aa48c7efe44a855e2ae2022-12-22T04:24:40ZengMDPI AGEntropy1099-43002011-10-0113111904191510.3390/e13111904Generalized Hamilton’s Principle for Inelastic Bodies Within Non-Equilibrium ThermodynamicsQiang YangKuang-Dai LengWithin 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].http://www.mdpi.com/1099-4300/13/11/1904/Hamilton’s principleinelastic bodyinternal variableinternal force |
| spellingShingle | Qiang Yang Kuang-Dai Leng Generalized Hamilton’s Principle for Inelastic Bodies Within Non-Equilibrium Thermodynamics Entropy Hamilton’s principle inelastic body internal variable internal force |
| title | Generalized Hamilton’s Principle for Inelastic Bodies Within Non-Equilibrium Thermodynamics |
| title_full | Generalized Hamilton’s Principle for Inelastic Bodies Within Non-Equilibrium Thermodynamics |
| title_fullStr | Generalized Hamilton’s Principle for Inelastic Bodies Within Non-Equilibrium Thermodynamics |
| title_full_unstemmed | Generalized Hamilton’s Principle for Inelastic Bodies Within Non-Equilibrium Thermodynamics |
| title_short | Generalized Hamilton’s Principle for Inelastic Bodies Within Non-Equilibrium Thermodynamics |
| title_sort | generalized hamilton s principle for inelastic bodies within non equilibrium thermodynamics |
| topic | Hamilton’s principle inelastic body internal variable internal force |
| url | http://www.mdpi.com/1099-4300/13/11/1904/ |
| work_keys_str_mv | AT qiangyang generalizedhamiltonsprincipleforinelasticbodieswithinnonequilibriumthermodynamics AT kuangdaileng generalizedhamiltonsprincipleforinelasticbodieswithinnonequilibriumthermodynamics |