Continuum thermodynamics.: Part I, Foundations /
This book is a unique presentation of thermodynamic methods of construction of continuous models. It is based on a uniform approach following from the entropy inequality and using Lagrange multipliers as auxiliary quantities in its evaluation. It covers a wide range of models - ideal gases, thermovi...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
[Hackensack] New Jersey :
World Scientific,
©2008.
|
| Schriftenreihe: | Series on advances in mathematics for applied sciences ;
v. 77. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book is a unique presentation of thermodynamic methods of construction of continuous models. It is based on a uniform approach following from the entropy inequality and using Lagrange multipliers as auxiliary quantities in its evaluation. It covers a wide range of models - ideal gases, thermoviscoelastic fluids, thermoelastic and thermoviscoelastic solids, plastic polycrystals, miscible and immiscible mixtures, and many others. The structure of phenomenological thermodynamics is justified by a systematic derivation from the Liouville equation, through the BBGKY-hierarchy-derived Boltzmann equation, to an extended thermodynamics. In order to simplify the reading, an extensive introduction to classical continuum mechanics and thermostatics is included. As a complementary volume to Part II, which will contain applications and examples, and to Part III, which will cover numerical methods, only a few simple examples are presented in this first Part. One exception is an extensive example of a linear poroelastic material because it will not appear in future Parts. |
| Beschreibung: | 1 online resource (x, 403 pages) : illustrations. |
| Bibliographie: | Includes bibliographical references (pages 373-395) and index. |
| ISBN: | 9789812835574 9812835571 |
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| 245 | 1 | 0 | |a Continuum thermodynamics. |n Part I, |p Foundations / |c Krzysztof Wilmanski. |
| 260 | |a [Hackensack] New Jersey : |b World Scientific, |c ©2008. | ||
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| 490 | 1 | |a Series on advances in mathematics for applied sciences ; |v v. 77 | |
| 504 | |a Includes bibliographical references (pages 373-395) and index. | ||
| 505 | 0 | |a 1. Introduction -- 2. Geometry. 2.1. Deformation gradient, material vectors. 2.2. Measures of deformation. 2.3. Extension, dilatation, shear. 2.4. Displacement. 2.5. Geometrical compatibility conditions. 2.6. Geometrical compatibility condition for singular surfaces -- 3. Kinematics. 3.1. Basic notions. 3.2. Objective time derivatives. 3.3. Boundaries, kinematical compatibility condition for singular surfaces -- 4. Balance equations. 4.1. Balance laws in Lagrangian description. 4.2. Balance laws in Eulerian description. 4.3. Extension on membranes and interfaces -- 5. Second law of thermodynamics. 5.1. Entropy inequality, thermodynamical admissibility. 5.2. Isotropy, material objectivity. 5.3. Materials with constraints. 5.4. Constitutive relations for various thermoelastic materials. 5.5. Proportionality theorem -- 6. Equilibrium Gibbs thermodynamics. 6.1. Thermostatics of gases. 6.2. Thermostatic theory of homogeneous mixtures -- 7. Kinetic theories. 7.1. Liouville equation. 7.2. BBGKY-hierarchy. 7.3. Boltzmann equation -- 8. Extended thermodynamics. 8.1. General structure. 8.2. Nonrelativistic ideal gases. 8.3. A few remarks on boundary conditions -- 9. Thermodynamical model of viscoelastic materials. 9.1. Foundations. 9.2. Thermodynamical admissibility. 9.3. Viscous fluids, linear viscoelastic solids. 9.4. Maxwell fluid, Rivlin-Ericksen fluids -- 10. Elasto-viscoplastic materials. 10.1. Preliminaries. 10.2. Local configurations. 10.3. Crystal plasticity of monocrystals. 10.4. Polycrystals and orientation distribution function. 10.5. Thermodynamical admissibility. 10.6. Two particular classes of models -- 11. Thermodynamics of miscible mixtures. 11.1. General structure and field equations. 11.2. Thermodynamical admissibility -- 12. Thermodynamics of immiscible mixtures: introduction and models without the field of porosity -- 13. Thermodynamics of poroelastic materials with the balance equation of porosity. 13.1. General structure. 13.2. Two-component poroelastic materials. 13.3. Linear models of saturated poroelastic materials. 13.4. Waves in poroelastic materials. 13.5. On adsorption in porous materials -- 14. Final remarks. | |
| 520 | |a This book is a unique presentation of thermodynamic methods of construction of continuous models. It is based on a uniform approach following from the entropy inequality and using Lagrange multipliers as auxiliary quantities in its evaluation. It covers a wide range of models - ideal gases, thermoviscoelastic fluids, thermoelastic and thermoviscoelastic solids, plastic polycrystals, miscible and immiscible mixtures, and many others. The structure of phenomenological thermodynamics is justified by a systematic derivation from the Liouville equation, through the BBGKY-hierarchy-derived Boltzmann equation, to an extended thermodynamics. In order to simplify the reading, an extensive introduction to classical continuum mechanics and thermostatics is included. As a complementary volume to Part II, which will contain applications and examples, and to Part III, which will cover numerical methods, only a few simple examples are presented in this first Part. One exception is an extensive example of a linear poroelastic material because it will not appear in future Parts. | ||
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| contents | 1. Introduction -- 2. Geometry. 2.1. Deformation gradient, material vectors. 2.2. Measures of deformation. 2.3. Extension, dilatation, shear. 2.4. Displacement. 2.5. Geometrical compatibility conditions. 2.6. Geometrical compatibility condition for singular surfaces -- 3. Kinematics. 3.1. Basic notions. 3.2. Objective time derivatives. 3.3. Boundaries, kinematical compatibility condition for singular surfaces -- 4. Balance equations. 4.1. Balance laws in Lagrangian description. 4.2. Balance laws in Eulerian description. 4.3. Extension on membranes and interfaces -- 5. Second law of thermodynamics. 5.1. Entropy inequality, thermodynamical admissibility. 5.2. Isotropy, material objectivity. 5.3. Materials with constraints. 5.4. Constitutive relations for various thermoelastic materials. 5.5. Proportionality theorem -- 6. Equilibrium Gibbs thermodynamics. 6.1. Thermostatics of gases. 6.2. Thermostatic theory of homogeneous mixtures -- 7. Kinetic theories. 7.1. Liouville equation. 7.2. BBGKY-hierarchy. 7.3. Boltzmann equation -- 8. Extended thermodynamics. 8.1. General structure. 8.2. Nonrelativistic ideal gases. 8.3. A few remarks on boundary conditions -- 9. Thermodynamical model of viscoelastic materials. 9.1. Foundations. 9.2. Thermodynamical admissibility. 9.3. Viscous fluids, linear viscoelastic solids. 9.4. Maxwell fluid, Rivlin-Ericksen fluids -- 10. Elasto-viscoplastic materials. 10.1. Preliminaries. 10.2. Local configurations. 10.3. Crystal plasticity of monocrystals. 10.4. Polycrystals and orientation distribution function. 10.5. Thermodynamical admissibility. 10.6. Two particular classes of models -- 11. Thermodynamics of miscible mixtures. 11.1. General structure and field equations. 11.2. Thermodynamical admissibility -- 12. Thermodynamics of immiscible mixtures: introduction and models without the field of porosity -- 13. Thermodynamics of poroelastic materials with the balance equation of porosity. 13.1. General structure. 13.2. Two-component poroelastic materials. 13.3. Linear models of saturated poroelastic materials. 13.4. Waves in poroelastic materials. 13.5. On adsorption in porous materials -- 14. Final remarks. |
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| dewey-ones | 536 - Heat |
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| dewey-search | 536/.7 |
| dewey-sort | 3536 17 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn557513691 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:16:58Z |
| institution | BVB |
| isbn | 9789812835574 9812835571 |
| language | English |
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| series | Series on advances in mathematics for applied sciences ; |
| series2 | Series on advances in mathematics for applied sciences ; |
| spelling | Wilmański, Krzysztof. http://id.loc.gov/authorities/names/n85383069 Continuum thermodynamics. Part I, Foundations / Krzysztof Wilmanski. [Hackensack] New Jersey : World Scientific, ©2008. 1 online resource (x, 403 pages) : illustrations. text txt rdacontent computer c rdamedia online resource cr rdacarrier Series on advances in mathematics for applied sciences ; v. 77 Includes bibliographical references (pages 373-395) and index. 1. Introduction -- 2. Geometry. 2.1. Deformation gradient, material vectors. 2.2. Measures of deformation. 2.3. Extension, dilatation, shear. 2.4. Displacement. 2.5. Geometrical compatibility conditions. 2.6. Geometrical compatibility condition for singular surfaces -- 3. Kinematics. 3.1. Basic notions. 3.2. Objective time derivatives. 3.3. Boundaries, kinematical compatibility condition for singular surfaces -- 4. Balance equations. 4.1. Balance laws in Lagrangian description. 4.2. Balance laws in Eulerian description. 4.3. Extension on membranes and interfaces -- 5. Second law of thermodynamics. 5.1. Entropy inequality, thermodynamical admissibility. 5.2. Isotropy, material objectivity. 5.3. Materials with constraints. 5.4. Constitutive relations for various thermoelastic materials. 5.5. Proportionality theorem -- 6. Equilibrium Gibbs thermodynamics. 6.1. Thermostatics of gases. 6.2. Thermostatic theory of homogeneous mixtures -- 7. Kinetic theories. 7.1. Liouville equation. 7.2. BBGKY-hierarchy. 7.3. Boltzmann equation -- 8. Extended thermodynamics. 8.1. General structure. 8.2. Nonrelativistic ideal gases. 8.3. A few remarks on boundary conditions -- 9. Thermodynamical model of viscoelastic materials. 9.1. Foundations. 9.2. Thermodynamical admissibility. 9.3. Viscous fluids, linear viscoelastic solids. 9.4. Maxwell fluid, Rivlin-Ericksen fluids -- 10. Elasto-viscoplastic materials. 10.1. Preliminaries. 10.2. Local configurations. 10.3. Crystal plasticity of monocrystals. 10.4. Polycrystals and orientation distribution function. 10.5. Thermodynamical admissibility. 10.6. Two particular classes of models -- 11. Thermodynamics of miscible mixtures. 11.1. General structure and field equations. 11.2. Thermodynamical admissibility -- 12. Thermodynamics of immiscible mixtures: introduction and models without the field of porosity -- 13. Thermodynamics of poroelastic materials with the balance equation of porosity. 13.1. General structure. 13.2. Two-component poroelastic materials. 13.3. Linear models of saturated poroelastic materials. 13.4. Waves in poroelastic materials. 13.5. On adsorption in porous materials -- 14. Final remarks. This book is a unique presentation of thermodynamic methods of construction of continuous models. It is based on a uniform approach following from the entropy inequality and using Lagrange multipliers as auxiliary quantities in its evaluation. It covers a wide range of models - ideal gases, thermoviscoelastic fluids, thermoelastic and thermoviscoelastic solids, plastic polycrystals, miscible and immiscible mixtures, and many others. The structure of phenomenological thermodynamics is justified by a systematic derivation from the Liouville equation, through the BBGKY-hierarchy-derived Boltzmann equation, to an extended thermodynamics. In order to simplify the reading, an extensive introduction to classical continuum mechanics and thermostatics is included. As a complementary volume to Part II, which will contain applications and examples, and to Part III, which will cover numerical methods, only a few simple examples are presented in this first Part. One exception is an extensive example of a linear poroelastic material because it will not appear in future Parts. Print version record. Thermodynamics. http://id.loc.gov/authorities/subjects/sh85134783 Thermodynamics https://id.nlm.nih.gov/mesh/D013816 Physics. Physical Sciences & Mathematics. Thermodynamics. Thermodynamique. thermodynamics. aat SCIENCE Mechanics Thermodynamics. bisacsh Thermodynamics fast Milieux continus, Mécanique des. ram Thermodynamique. ram has work: Part I Foundations Continuum thermodynamics (Text) https://id.oclc.org/worldcat/entity/E39PCGbktGqqvQ4FJPmdMDD3w3 https://id.oclc.org/worldcat/ontology/hasWork Print version: Wilmanski, Krzysztof. Continuum thermodynamics. Part I, Foundations. [Hackensack] New Jersey ; London ; Singapore [etc.] : World Scientific, 2008 9789812835567 (OCoLC)494874895 Series on advances in mathematics for applied sciences ; v. 77. http://id.loc.gov/authorities/names/n90710999 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=305242 Volltext |
| spellingShingle | Wilmański, Krzysztof Continuum thermodynamics. Series on advances in mathematics for applied sciences ; 1. Introduction -- 2. Geometry. 2.1. Deformation gradient, material vectors. 2.2. Measures of deformation. 2.3. Extension, dilatation, shear. 2.4. Displacement. 2.5. Geometrical compatibility conditions. 2.6. Geometrical compatibility condition for singular surfaces -- 3. Kinematics. 3.1. Basic notions. 3.2. Objective time derivatives. 3.3. Boundaries, kinematical compatibility condition for singular surfaces -- 4. Balance equations. 4.1. Balance laws in Lagrangian description. 4.2. Balance laws in Eulerian description. 4.3. Extension on membranes and interfaces -- 5. Second law of thermodynamics. 5.1. Entropy inequality, thermodynamical admissibility. 5.2. Isotropy, material objectivity. 5.3. Materials with constraints. 5.4. Constitutive relations for various thermoelastic materials. 5.5. Proportionality theorem -- 6. Equilibrium Gibbs thermodynamics. 6.1. Thermostatics of gases. 6.2. Thermostatic theory of homogeneous mixtures -- 7. Kinetic theories. 7.1. Liouville equation. 7.2. BBGKY-hierarchy. 7.3. Boltzmann equation -- 8. Extended thermodynamics. 8.1. General structure. 8.2. Nonrelativistic ideal gases. 8.3. A few remarks on boundary conditions -- 9. Thermodynamical model of viscoelastic materials. 9.1. Foundations. 9.2. Thermodynamical admissibility. 9.3. Viscous fluids, linear viscoelastic solids. 9.4. Maxwell fluid, Rivlin-Ericksen fluids -- 10. Elasto-viscoplastic materials. 10.1. Preliminaries. 10.2. Local configurations. 10.3. Crystal plasticity of monocrystals. 10.4. Polycrystals and orientation distribution function. 10.5. Thermodynamical admissibility. 10.6. Two particular classes of models -- 11. Thermodynamics of miscible mixtures. 11.1. General structure and field equations. 11.2. Thermodynamical admissibility -- 12. Thermodynamics of immiscible mixtures: introduction and models without the field of porosity -- 13. Thermodynamics of poroelastic materials with the balance equation of porosity. 13.1. General structure. 13.2. Two-component poroelastic materials. 13.3. Linear models of saturated poroelastic materials. 13.4. Waves in poroelastic materials. 13.5. On adsorption in porous materials -- 14. Final remarks. Thermodynamics. http://id.loc.gov/authorities/subjects/sh85134783 Thermodynamics https://id.nlm.nih.gov/mesh/D013816 Physics. Physical Sciences & Mathematics. Thermodynamics. Thermodynamique. thermodynamics. aat SCIENCE Mechanics Thermodynamics. bisacsh Thermodynamics fast Milieux continus, Mécanique des. ram Thermodynamique. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85134783 https://id.nlm.nih.gov/mesh/D013816 |
| title | Continuum thermodynamics. |
| title_auth | Continuum thermodynamics. |
| title_exact_search | Continuum thermodynamics. |
| title_full | Continuum thermodynamics. Part I, Foundations / Krzysztof Wilmanski. |
| title_fullStr | Continuum thermodynamics. Part I, Foundations / Krzysztof Wilmanski. |
| title_full_unstemmed | Continuum thermodynamics. Part I, Foundations / Krzysztof Wilmanski. |
| title_short | Continuum thermodynamics. |
| title_sort | continuum thermodynamics foundations |
| topic | Thermodynamics. http://id.loc.gov/authorities/subjects/sh85134783 Thermodynamics https://id.nlm.nih.gov/mesh/D013816 Physics. Physical Sciences & Mathematics. Thermodynamics. Thermodynamique. thermodynamics. aat SCIENCE Mechanics Thermodynamics. bisacsh Thermodynamics fast Milieux continus, Mécanique des. ram Thermodynamique. ram |
| topic_facet | Thermodynamics. Thermodynamics Physics. Physical Sciences & Mathematics. Thermodynamique. thermodynamics. SCIENCE Mechanics Thermodynamics. Milieux continus, Mécanique des. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=305242 |
| work_keys_str_mv | AT wilmanskikrzysztof continuumthermodynamicsparti |