Thermodynamics of materials with memory : theory and applications / / Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden

• Autore: Amendola Giovambattista
• Pubblicazione: Cham, Switzerland : , : Springer, , [2021]; ©2021
• Edizione: Second edition.
• Descrizione fisica: 1 online resource (756 pages)
• Disciplina: 621.4021
• Soggetto topico: Thermodynamics - Mathematical models; Termodinàmica; Materials intel·ligents; Models matemàtics; Mecànica dels medis continus
• Soggetto genere / forma: Llibres electrònics
• Persona (resp. second.): FabrizioMauro <1940->; GoldenJ. M <1945-> (John M.)
• Nota di contenuto: Intro -- Preface to Second Edition -- Preface to First Edition -- Contents -- Introduction -- Part I Continuum Mechanics and Classical Materials -- 1 Introduction to Continuum Mechanics -- 1.1 Introduction -- 1.2 Kinematics -- 1.2.1 Continuous Bodies: Deformations-Strain Tensors -- 1.2.2 Small Deformations: The Saint-Venant Compatibility Conditions -- 1.2.3 Transformation of Areas and Volumes: Transport Theorems -- 1.3 Principles of Continuum Mechanics -- 1.3.1 Principle of Conservation of Mass -- 1.3.2 Momentum Balance Principles -- 1.3.3 Consequences of Momentum Balance Laws -- 1.3.4 The Piola-Kirchhoff Stresses -- 1.4 Constitutive Equations -- 1.4.1 Objectivity -- 1.4.2 Principle of Material Objectivity -- 1.4.3 Fading Memory -- 2 Materials with Constitutive Equations That Are Local in Time -- 2.1 Introduction -- 2.2 Fluids: Ideal Fluids -- 2.2.1 Elastic Fluids -- 2.2.2 Newtonian Fluids: The Navier-Stokes Equations -- 2.2.3 Uniqueness of Solutions -- 2.3 Elastic Solids -- 2.3.1 Finite Elasticity -- 2.3.2 Hyperelastic Bodies -- 2.4 Linear Elasticity -- 2.4.1 Linear Elastostatics -- 2.4.2 Saint-Venant's Problem -- Part II Continuum Thermodynamics and Constitutive Equations of Mechanics and Electromagnetism -- 3 Principles of Thermodynamics -- 3.1 Heat Equation -- 3.2 Definition of a Material as a Dynamical System -- 3.3 First Principle of Thermodynamics -- 3.4 Second Principle of Thermodynamics -- 3.4.1 The Absolute Temperature Scale -- 3.4.2 Entropy Action -- 3.5 Applications to Elastic Bodies -- 3.6 Thermodynamic Restrictions for Viscous Fluids -- 3.7 Principles of Thermodynamics for Nonsimple Materials -- 3.7.1 First Law of Thermodynamics -- 3.7.2 Second Law of Thermodynamics -- 4 Free Energies and the Dissipation Principle -- 4.1 Axiomatic Formulation of Thermodynamics -- 4.2 Minimum and Maximum Free Energies. ; 5 Thermodynamics of Materials with Memory -- 5.1 Derivation of the Constitutive Equations -- 5.1.1 Required Properties of a Free Energy -- 5.1.2 Periodic Histories for General Materials -- 5.1.3 Constraints on the Nonuniqueness of the Free Energy -- 5.2 The Maximum Recoverable Work for General Materials -- 5.3 Generation of New Free Energies -- 6 Thermoelectromagnetism of Continuous Media -- 6.1 Electromagnetism of Continuous Media -- 6.1.1 Balance Laws in Electromagnetic Media -- 6.1.2 Constitutive Equations -- 6.1.3 Boundary Conditions -- 6.1.4 Balance of Energy and the First Law of Thermodynamics -- 6.1.5 Second Law of Thermodynamics and the Clausius-Duhem Inequality -- 6.1.6 Thermodynamics of Nonlocal Materials -- 6.1.7 Two Potentials Related to the Electromagnetic Fields -- 6.2 Electromagnetic Systems with Memory -- 6.2.1 Memory Effects Justified by Waves in Water -- 6.2.2 Some Simple Models to Study Material Behavior -- 6.2.2.1 Dielectrics -- 6.2.2.2 Magnetic Materials -- 6.2.2.3 Metals -- 6.2.2.4 The Ionosphere -- 6.2.3 The Clausius-Duhem Inequality and Its Consequences -- 6.3 Thermodynamics of Simple Electromagnetic Materials -- 6.3.1 Electromagnetic Materials -- 6.3.2 Materials with Fading Memory -- 6.3.2.1 Dielectrics with Memory -- 6.3.2.2 Conductors with Memory -- 6.3.3 Thermodynamic Laws in Terms of Cycles -- Part III Free Energies for Materials with Linear Memory -- 7 A Linear Memory Model -- 7.1 A Quadratic Model for Free Energies -- 7.1.1 Constitutive Relations -- 7.1.2 Dissipation Rate -- 7.1.3 Complete Material Characterization -- 7.1.4 Linear Equilibrium Response -- 7.1.5 Time-Independent Eigenspaces -- 7.1.6 Short-Term Memory -- 7.2 Constitutive Equations in the Frequency Domain -- 7.2.1 Sinusoidal Histories for the General Theory -- 7.2.2 Properties of L' -- 7.2.3 Frequency-Domain Representation of the History. ; 7.2.4 Constitutive Equations in Terms of Frequency-Domain Quantities -- 7.3 The Form of the Generalized Relaxation Function -- 7.3.1 Isolated Singularities -- 7.3.2 Branch Cuts -- 7.3.3 Essential Singularities -- 7.4 Minimal States in the Nonisothermal Case -- 7.5 Forms of the Work Function -- 8 Viscoelastic Solids and Fluids -- 8.1 Linear Viscoelastic Solids -- 8.1.1 Thermodynamic Restrictions for Viscoelastic Solids -- 8.2 Decomposition of Stress -- 8.3 Equivalence and Minimal States -- 8.4 State and History for Exponential-Type Relaxation Functions -- 8.5 Inversion of Constitutive Relations -- 8.6 Linear Viscoelastic Free Energies as Quadratic Functionals -- 8.6.1 General Forms of a Free Energy in Terms of Stress -- 8.6.2 The Work Function as a Free Energy -- 8.7 The Relaxation Property and a Work Function Norm -- 8.8 Viscoelastic Fluids -- 8.9 Compressible Viscoelastic Fluids -- 8.9.1 A Particular Class of Compressible Fluids -- 8.9.2 Representation of Free Energies for Compressible Fluids -- 8.9.3 Thermodynamic Restrictions for Compressible Fluids -- 8.10 Incompressible Viscoelastic Fluids -- 8.10.1 Thermodynamic Restrictions for Incompressible Viscoelastic Fluids -- 8.10.2 The Mechanical Work -- 8.10.3 Maximum Free Energy for Incompressible Fluids -- 9 Heat Conductors -- 9.1 Constitutive Equations for Rigid Heat Conductors -- 9.1.1 States in Terms of t(s) and gt -- 9.1.2 Constitutive Equations in Terms of States and Processes -- 9.1.3 Equivalent Histories and Minimal States -- 9.2 Thermodynamic Constraints for Rigid Heat Conductors -- 9.3 Thermal Work -- 9.3.1 Integrated Histories for Isotropic Heat Conductors -- 9.3.2 Finite Work Processes and w-Equivalence for States -- 9.3.3 Free Energies as Quadratic Functionals for Rigid Heat Conductors -- 9.3.4 The Work Function -- 10 Free Energies on Special Classes of Material. ; 10.1 The General Nonisothermal Case -- 10.1.1 The Graffi-Volterra Free Energy -- 10.1.2 Dill/Staverman-Schwarzl Free Energy -- 10.1.3 Single-Integral Quadratic Functionals of It -- 10.2 Free Energies for Restricted Classes of Solids -- 10.3 Free Energies for Restricted Classes of Fluids -- 10.4 Free Pseudoenergies for Restricted Classes of RigidHeat Conductors -- 11 The Minimum Free Energy -- 11.1 Factorization of Positive Definite Tensors -- 11.1.1 The Scalar Case -- 11.2 Derivation of the Form of the Minimum Free Energy -- 11.2.1 A Variational Approach -- 11.2.2 The Wiener-Hopf Method -- 11.2.3 Histories Rather Than Relative Histories -- 11.2.4 Confirmation That ψm Is a Free Energy -- 11.2.5 Double Frequency Integral Form -- 11.3 Characterization of the Minimal State in the Frequency Domain -- 11.4 The Space of States and Processes -- 11.5 Limiting Properties of the Optimal Future Continuation -- 11.6 Time-Independent Eigenspaces -- 11.7 The Minimum Free Energy for Sinusoidal Histories -- 11.8 Example: Viscoelastic Materials -- 11.9 Explicit Forms of the Minimum Free Energy for Discrete-Spectrum Materials -- 12 Representation of the Minimum Free Energy in the Time Domain -- 12.1 The Minimum Free Energy in Terms of Time-Domain Relative Histories -- 12.2 The Minimum Free Energy Expressed in Terms of It -- 13 Minimum Free Energy for Viscoelastic Solids, Fluids, and Heat Conductors -- 13.1 Maximum Recoverable Work for Solids -- 13.1.1 Minimum Free Energy for Solids -- 13.1.2 Minimum Free Energies in Terms of Stress History -- 13.2 Maximum Recoverable Work for Fluids -- 13.2.1 The Minimum Free Energy for Fluids -- 13.3 The Minimum Free Energy for Incompressible Fluids -- 13.3.1 The Minimum Free Energy in Terms of It -- 13.4 The Maximum Recoverable Work for Heat Conductors -- 13.4.1 The Minimum Free Energy for Heat Conductors. ; 13.4.2 The Discrete-Spectrum Model for Heat Conductors -- 14 The Minimum Free Energy for a Continuous-Spectrum Material -- 14.1 Introduction -- 14.2 Continuous-Spectrum Materials -- 14.3 Factorization of H for a Continuous-Spectrum Material -- 14.3.1 Properties of the Factorization Formulas -- 14.4 The Minimum Free Energy -- 14.5 An Alternative Approach -- 14.6 Minimal States -- 15 The Minimum Free Energy for a Finite-Memory Material -- 15.1 Introduction -- 15.2 Finite Memory -- 15.3 The History Dependence of the Minimum Free Energy -- 15.4 Factorization of H(ω) -- 15.5 Explicit Forms of the Minimum Free Energy -- 16 Free Energies for the Case of Isolated Singularities -- 16.1 Constitutive Relations, Histories, and Free Energy Properties for the Scalar Case -- 16.1.1 Frequency-Domain Quantities for the Scalar Case -- 16.1.2 Defining Properties of Free Energies -- 16.2 Materials with Only Isolated Singularities -- 16.3 Free Energies as Discrete Quadratic Forms -- 16.3.1 Discrete-Spectrum Materials -- 16.4 The Minimum and Related Free Energies -- 16.5 Equivalent States and the Maximum Free Energy -- 16.5.1 Minimal States -- 16.5.1.1 Explicit Examples of Minimal States -- 16.5.1.2 The Maximum Free Energy -- 16.6 Scalar Product Notation for ψf and Related Quantities as Quadratic Functionals -- 16.6.1 Confirmation That ψf Is a Free Energy -- 16.7 Asymptotic Behavior and Discontinuities -- 16.8 Partial Orderings of the ψf -- 16.9 Explicit Forms for ψf -- 16.9.1 Explicit Forms of the Minimum and Related Free Energies for Discrete-Spectrum Materials -- 16.10 The Central Free Energy and Related Dissipation -- 16.11 Plots of Free Energies -- 17 Constructing Free Energies for Materials with Memory -- 17.1 Two Equivalent Interpretations of the Set of Free Energies -- 17.2 Unique Characterization of Materials with Memory -- 17.3 Quadratic Models for Free Energies. ; 17.3.1 A Single-Integral Model.
• Titolo autorizzato: Thermodynamics of materials with memory
• ISBN: 3-030-80534-4
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910506381203321
• Lo trovi qui: Univ. Federico II