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MARC Lista (tabellare)
Collected papers in honor Yoshihiro Shibata / / Tohru Ozawa, editor
Collected papers in honor Yoshihiro Shibata / / Tohru Ozawa, editor
Pubbl/distr/stampa Cham, Switzerland : , : Birkhäuser, , [2023]
Descrizione fisica 1 online resource (396 pages)
Disciplina 531
Soggetto topico Continuum mechanics
Differential equations
Mecànica dels medis continus
Equacions diferencials
Soggetto genere / forma Llibres electrònics
ISBN 9783031192524
9783031192517
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Contents -- Preface -- References -- Global Wellposedness of the Primitive Equations with Nonlinear Equation of State in Critical Spaces -- Abstract -- 1. Introduction -- 2. Preliminaries -- 3. Typical Ocean Densities -- 3.1. Linear Density -- 3.2. Equation of State by TEOS-10 -- 3.3. Equation of State by McDongall-Jacket-Wright-Feistel -- 3.4. Equation of State by UNESCO-80 -- 4. Main Result -- 5. Estimates for the Local Existence -- 6. A Priori Estimates -- 7. Proof of Theorem 4.1 -- 7.1. Local Wellposedness -- 7.2. Global Wellposedness -- Appendix A. Semilinear Evolution Equations and Maximal Lr-Regularity -- References -- On the Global Existence for the Compressible Euler-Riesz System -- Abstract -- Introduction -- 1. Main Results -- 2. A Local in Time Result for Non-decaying Data -- 2.1. A Priori Estimates -- 2.2. About the Proof of Existence -- 2.3. Uniqueness -- 3. A Global Existence Result -- 3.1. A Priori Estimates -- 3.2. Existence -- 3.3. The Proof of Uniqueness -- 3.4. Instability of Nontrivial Static Solutions in the Attractive Case -- 4. About Ideal Gases -- 4.1. Local Existence -- 4.2. Global Existence -- 4.3. Remark on Static Solutions -- Appendix -- Acknowledgements -- References -- Rotation Problem for a Two-Phase Drop -- Abstract -- 1. Introduction -- 2. Linear Problem -- 3. The Nonlinear Problem -- References -- On the Stokes-Type Resolvent Problem Associated with Time-Periodic Flow Around a Rotating Obstacle -- Abstract -- 1. Introduction -- 2. Notation -- 3. Main Results -- 4. The Resolvent Problem in the Whole Space -- 5. The Resolvent Problem in an Exterior Domain -- 6. The Time-Periodic Problem -- References -- Euler System with a Polytropic Equation of State as a Vanishing Viscosity Limit -- Abstract -- 1. Introduction -- 2. Preliminary Material -- 2.1. Mathematical Theory of the Closed System.
2.2. Transport Coefficients -- 2.3. Equation of State -- 2.4. Relative Energy -- 3. Main Results -- 3.1. Unconditional Convergence in the Absence of Boundary Layer -- 3.2. Conditional Result: Viscous Boundary Layer -- 4. Consistency of the Vanishing Dissipation/Radiation Approximation -- 4.1. Temperature for the Euler System -- 4.2. Consistency -- 4.2.1. Viscous Stress Consistency -- 4.2.2. Heat Flux Consistency -- 4.2.3. Radiation Entropy Convective Flux Consistency -- 5. Convergence -- 5.1. Velocity Regularization -- 5.2. Application of the Relative Energy Inequality -- 5.3. Integrals Controlled by the Consistency Estimates -- 5.4. Integrals Independent of the Boundary Layer -- 5.5. Boundary Layer -- 5.5.1. Viscous Stress -- 5.5.2. Convective Term -- 5.6. Strong Convergence -- References -- On the Hydrostatic Approximation of Compressible Anisotropic Navier-Stokes Equations-Rigorous Justification -- Abstract -- 1. Introduction -- 2. Preliminaries -- 3. Main Result -- 3.1. Dissipative Weak Solutions of CNS -- 3.2. Strong Solution of CPE -- 3.3. Versatile Relative Entropy Inequality -- 3.4. Main Result -- 4. Convergence -- 4.1. Main Idea of Proof -- 4.2. Step 1 -- 4.3. Step 2 -- 4.4. Step 3 -- Acknowledgements -- References -- A Route to Chaos in Rayleigh-Bénard Heat Convection -- Abstract -- 1. Introduction -- 2. linear Stability and Critical Rayleigh Number -- 3. Routes to Chaos -- 3.1. Roll Solutions on Bifurcation Branches in the Large -- 3.2. Time Evolution of Roll Solutions and the Secondary Hopf Bifurcation -- 3.3. Concluding Remark -- Acknowledgements -- References -- Existence of Weak Solution to the Nonstationary Navier-Stokes Equations Approximated by Pressure Stabilization Method -- Abstract -- 1. Introduction -- 2. Notations and Main Results -- 3. Preliminaries -- 4. Proof of Main Results -- Acknowledgements -- References.
Resolvent Estimates for a Compressible Fluid Model of Korteweg Type and Their Application -- Abstract -- 1. Introduction -- 2. Notation and Main Results -- 2.1. Notation -- 2.2. Main Results -- 3. Preliminaries -- 3.1. Some Inequalities -- 3.2. Compact Embeddings -- 3.3. Results of the Large Resolvent Parameter -- 3.4. Maximal Regularity -- 4. The Problem in Bounded Domains -- 4.1. Existence of Solutions -- 4.2. Uniqueness of Solutions -- 4.3. A Priori Estimates -- 4.4. Proof of Theorem 2.5 -- 4.5. Proof of Theorem 2.6 -- 5. The Whole Space Problem -- 5.1. Representation Formulas of Solutions -- 5.2. Estimates of P(ξ,λ) for γ=0. -- 5.3. Estimates of P(ξ,λ) for γ> -- 0. -- 5.4. Proof of Theorem 5.1 -- 6. The Problem in Exterior Domains -- 6.1. Construction of Parametrix -- 6.2. Uniqueness of Solutions -- 6.3. A Priori Estimates -- 6.4. An Auxiliary Problem -- 6.5. Proof of Theorem 2.1 -- 7. Application to a Nonlinear Problem -- 7.1. Generation of an Analytic C0-Semigroup -- 7.2. Maximal Regularity with Exponential Stability -- 7.3. Estimates of Nonlinear Terms -- 7.4. Global Solvability of the Nonlinear Problem -- References -- Rate of the Enhanced Dissipation for the Two-jet Kolmogorov Type Flow on the Unit Sphere -- Abstract -- 1. Introduction -- 2. Preliminaries -- 3. Analysis of the Linearized Operator -- 3.1. Settings and Basic Results -- 3.2. Verification of Assumption 4.6 -- 3.3. Estimates for the Semigroup -- 4. Abstract Results -- 5. Appendix: Basic Formulas of Differential Geometry -- Acknowledgements -- References -- Reacting Multi-component Fluids: Regular Solutions in Lorentz Spaces -- Abstract -- 1. Introduction -- 2. Functional Spaces and the Main Result -- 3. Auxiliary Results and Linear Theory -- 4. A Priori Estimates -- 4.1. Velocity Bounds -- 4.2. Estimates for the Density -- 5. Existence -- Acknowledgements -- References.
Global Well Posedness for a Q-tensor Model of Nematic Liquid Crystals -- Abstract -- 1. Introduction -- 2. Maximal Lp-Lq Regularity -- 2.1. mathcalR-boundedness of Solution Operators -- 2.2. A Proof of Theorem 2.1 -- 3. Decay Property of Solutions to the Linearized Problem -- 3.1. Decay Estimates for d -- 3.2. Decay Estimates for U and mathbbQ -- 3.2.1. Analysis of Low Frequency Parts -- 3.2.2. Analysis of High Frequency Parts -- 4. A Proof of Theorem 1.1 -- 4.1. Analysis of Time Shifted Equations -- 4.2. Analysis of Compensation Equations -- 4.2.1. Estimates of Spatial Derivatives in Lp-Lq -- 4.2.2. Estimates of Time Derivatives in Lp-Lq -- 4.2.3. Estimates of the Lower Order Term in Linfty-Lq -- 4.3. Conclusion -- References -- Maximal Regularity for Compressible Two-Fluid System -- Abstract -- 1. Introduction -- 1.1. Notation -- 1.2. Main Results -- 1.3. Discussion -- 2. Lagrangian Coordinates -- 3. Local Well-Posedness -- 3.1. Linearization Around the Initial Condition -- 3.2. Maximal Regularity -- 3.3. Preliminary Estimates -- 3.4. Estimate of the Right Hand Side of (3.3) -- 3.5. Contraction Argument-Proof of Theorem 1.1 -- 4. Global Well-Posedness -- 4.1. Linearization Around the Constant State -- 4.2. Exponential Decay -- 4.3. Bounds for Nonlinearities -- 4.4. Proof of Theorem 1.2 -- Appendix -- Acknowledgements -- References -- Steady Compressible Navier-Stokes-Fourier Equations with Dirichlet Boundary Condition for the Temperature -- Abstract -- 1. Introduction -- 2. Formulation of the Problem: Main Result -- 3. Weak Compactness of Weak and Variational Entropy Ballistic Solutions -- 3.1. A Priori Estimates -- 3.2. Weak Compactness -- 4. Construction of the Solution -- References -- A Slightly Supercritical Condition of Regularity of Axisymmetric Solutions to the Navier-Stokes Equations -- Abstract -- 1. Introduction -- 2. Auxiliary Facts.
3. Proof of Proposition 1.4 -- 4. Proof of Theorem 1.3 -- Acknowledgements -- References -- Spatial Pointwise Behavior of Time-Periodic Navier-Stokes Flow Induced by Oscillation of a Moving Obstacle -- Abstract -- 1. Introduction -- 2. Results -- 2.1. Notation -- 2.2. Evolution Operator -- 2.3. Main Results -- 3. Proof of Theorem 2.1 -- 3.1. Weak Form of the Integral Equation -- 3.2. Regularity in x -- 3.3. Regularity in t and the Pressure -- 4. Proof of Theorem 2.2 -- 4.1. Reduction to the Whole Space Problem -- 4.2. Integral Equation for the Whole Space Problem -- 4.3. Reconstruction Procedure -- References.
Record Nr. UNINA-9910633925403321
Cham, Switzerland : , : Birkhäuser, , [2023]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Collected papers in honor Yoshihiro Shibata / / Tohru Ozawa, editor
Collected papers in honor Yoshihiro Shibata / / Tohru Ozawa, editor
Pubbl/distr/stampa Cham, Switzerland : , : Birkhäuser, , [2023]
Descrizione fisica 1 online resource (396 pages)
Disciplina 531
Soggetto topico Continuum mechanics
Differential equations
Mecànica dels medis continus
Equacions diferencials
Soggetto genere / forma Llibres electrònics
ISBN 9783031192524
9783031192517
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Contents -- Preface -- References -- Global Wellposedness of the Primitive Equations with Nonlinear Equation of State in Critical Spaces -- Abstract -- 1. Introduction -- 2. Preliminaries -- 3. Typical Ocean Densities -- 3.1. Linear Density -- 3.2. Equation of State by TEOS-10 -- 3.3. Equation of State by McDongall-Jacket-Wright-Feistel -- 3.4. Equation of State by UNESCO-80 -- 4. Main Result -- 5. Estimates for the Local Existence -- 6. A Priori Estimates -- 7. Proof of Theorem 4.1 -- 7.1. Local Wellposedness -- 7.2. Global Wellposedness -- Appendix A. Semilinear Evolution Equations and Maximal Lr-Regularity -- References -- On the Global Existence for the Compressible Euler-Riesz System -- Abstract -- Introduction -- 1. Main Results -- 2. A Local in Time Result for Non-decaying Data -- 2.1. A Priori Estimates -- 2.2. About the Proof of Existence -- 2.3. Uniqueness -- 3. A Global Existence Result -- 3.1. A Priori Estimates -- 3.2. Existence -- 3.3. The Proof of Uniqueness -- 3.4. Instability of Nontrivial Static Solutions in the Attractive Case -- 4. About Ideal Gases -- 4.1. Local Existence -- 4.2. Global Existence -- 4.3. Remark on Static Solutions -- Appendix -- Acknowledgements -- References -- Rotation Problem for a Two-Phase Drop -- Abstract -- 1. Introduction -- 2. Linear Problem -- 3. The Nonlinear Problem -- References -- On the Stokes-Type Resolvent Problem Associated with Time-Periodic Flow Around a Rotating Obstacle -- Abstract -- 1. Introduction -- 2. Notation -- 3. Main Results -- 4. The Resolvent Problem in the Whole Space -- 5. The Resolvent Problem in an Exterior Domain -- 6. The Time-Periodic Problem -- References -- Euler System with a Polytropic Equation of State as a Vanishing Viscosity Limit -- Abstract -- 1. Introduction -- 2. Preliminary Material -- 2.1. Mathematical Theory of the Closed System.
2.2. Transport Coefficients -- 2.3. Equation of State -- 2.4. Relative Energy -- 3. Main Results -- 3.1. Unconditional Convergence in the Absence of Boundary Layer -- 3.2. Conditional Result: Viscous Boundary Layer -- 4. Consistency of the Vanishing Dissipation/Radiation Approximation -- 4.1. Temperature for the Euler System -- 4.2. Consistency -- 4.2.1. Viscous Stress Consistency -- 4.2.2. Heat Flux Consistency -- 4.2.3. Radiation Entropy Convective Flux Consistency -- 5. Convergence -- 5.1. Velocity Regularization -- 5.2. Application of the Relative Energy Inequality -- 5.3. Integrals Controlled by the Consistency Estimates -- 5.4. Integrals Independent of the Boundary Layer -- 5.5. Boundary Layer -- 5.5.1. Viscous Stress -- 5.5.2. Convective Term -- 5.6. Strong Convergence -- References -- On the Hydrostatic Approximation of Compressible Anisotropic Navier-Stokes Equations-Rigorous Justification -- Abstract -- 1. Introduction -- 2. Preliminaries -- 3. Main Result -- 3.1. Dissipative Weak Solutions of CNS -- 3.2. Strong Solution of CPE -- 3.3. Versatile Relative Entropy Inequality -- 3.4. Main Result -- 4. Convergence -- 4.1. Main Idea of Proof -- 4.2. Step 1 -- 4.3. Step 2 -- 4.4. Step 3 -- Acknowledgements -- References -- A Route to Chaos in Rayleigh-Bénard Heat Convection -- Abstract -- 1. Introduction -- 2. linear Stability and Critical Rayleigh Number -- 3. Routes to Chaos -- 3.1. Roll Solutions on Bifurcation Branches in the Large -- 3.2. Time Evolution of Roll Solutions and the Secondary Hopf Bifurcation -- 3.3. Concluding Remark -- Acknowledgements -- References -- Existence of Weak Solution to the Nonstationary Navier-Stokes Equations Approximated by Pressure Stabilization Method -- Abstract -- 1. Introduction -- 2. Notations and Main Results -- 3. Preliminaries -- 4. Proof of Main Results -- Acknowledgements -- References.
Resolvent Estimates for a Compressible Fluid Model of Korteweg Type and Their Application -- Abstract -- 1. Introduction -- 2. Notation and Main Results -- 2.1. Notation -- 2.2. Main Results -- 3. Preliminaries -- 3.1. Some Inequalities -- 3.2. Compact Embeddings -- 3.3. Results of the Large Resolvent Parameter -- 3.4. Maximal Regularity -- 4. The Problem in Bounded Domains -- 4.1. Existence of Solutions -- 4.2. Uniqueness of Solutions -- 4.3. A Priori Estimates -- 4.4. Proof of Theorem 2.5 -- 4.5. Proof of Theorem 2.6 -- 5. The Whole Space Problem -- 5.1. Representation Formulas of Solutions -- 5.2. Estimates of P(ξ,λ) for γ=0. -- 5.3. Estimates of P(ξ,λ) for γ> -- 0. -- 5.4. Proof of Theorem 5.1 -- 6. The Problem in Exterior Domains -- 6.1. Construction of Parametrix -- 6.2. Uniqueness of Solutions -- 6.3. A Priori Estimates -- 6.4. An Auxiliary Problem -- 6.5. Proof of Theorem 2.1 -- 7. Application to a Nonlinear Problem -- 7.1. Generation of an Analytic C0-Semigroup -- 7.2. Maximal Regularity with Exponential Stability -- 7.3. Estimates of Nonlinear Terms -- 7.4. Global Solvability of the Nonlinear Problem -- References -- Rate of the Enhanced Dissipation for the Two-jet Kolmogorov Type Flow on the Unit Sphere -- Abstract -- 1. Introduction -- 2. Preliminaries -- 3. Analysis of the Linearized Operator -- 3.1. Settings and Basic Results -- 3.2. Verification of Assumption 4.6 -- 3.3. Estimates for the Semigroup -- 4. Abstract Results -- 5. Appendix: Basic Formulas of Differential Geometry -- Acknowledgements -- References -- Reacting Multi-component Fluids: Regular Solutions in Lorentz Spaces -- Abstract -- 1. Introduction -- 2. Functional Spaces and the Main Result -- 3. Auxiliary Results and Linear Theory -- 4. A Priori Estimates -- 4.1. Velocity Bounds -- 4.2. Estimates for the Density -- 5. Existence -- Acknowledgements -- References.
Global Well Posedness for a Q-tensor Model of Nematic Liquid Crystals -- Abstract -- 1. Introduction -- 2. Maximal Lp-Lq Regularity -- 2.1. mathcalR-boundedness of Solution Operators -- 2.2. A Proof of Theorem 2.1 -- 3. Decay Property of Solutions to the Linearized Problem -- 3.1. Decay Estimates for d -- 3.2. Decay Estimates for U and mathbbQ -- 3.2.1. Analysis of Low Frequency Parts -- 3.2.2. Analysis of High Frequency Parts -- 4. A Proof of Theorem 1.1 -- 4.1. Analysis of Time Shifted Equations -- 4.2. Analysis of Compensation Equations -- 4.2.1. Estimates of Spatial Derivatives in Lp-Lq -- 4.2.2. Estimates of Time Derivatives in Lp-Lq -- 4.2.3. Estimates of the Lower Order Term in Linfty-Lq -- 4.3. Conclusion -- References -- Maximal Regularity for Compressible Two-Fluid System -- Abstract -- 1. Introduction -- 1.1. Notation -- 1.2. Main Results -- 1.3. Discussion -- 2. Lagrangian Coordinates -- 3. Local Well-Posedness -- 3.1. Linearization Around the Initial Condition -- 3.2. Maximal Regularity -- 3.3. Preliminary Estimates -- 3.4. Estimate of the Right Hand Side of (3.3) -- 3.5. Contraction Argument-Proof of Theorem 1.1 -- 4. Global Well-Posedness -- 4.1. Linearization Around the Constant State -- 4.2. Exponential Decay -- 4.3. Bounds for Nonlinearities -- 4.4. Proof of Theorem 1.2 -- Appendix -- Acknowledgements -- References -- Steady Compressible Navier-Stokes-Fourier Equations with Dirichlet Boundary Condition for the Temperature -- Abstract -- 1. Introduction -- 2. Formulation of the Problem: Main Result -- 3. Weak Compactness of Weak and Variational Entropy Ballistic Solutions -- 3.1. A Priori Estimates -- 3.2. Weak Compactness -- 4. Construction of the Solution -- References -- A Slightly Supercritical Condition of Regularity of Axisymmetric Solutions to the Navier-Stokes Equations -- Abstract -- 1. Introduction -- 2. Auxiliary Facts.
3. Proof of Proposition 1.4 -- 4. Proof of Theorem 1.3 -- Acknowledgements -- References -- Spatial Pointwise Behavior of Time-Periodic Navier-Stokes Flow Induced by Oscillation of a Moving Obstacle -- Abstract -- 1. Introduction -- 2. Results -- 2.1. Notation -- 2.2. Evolution Operator -- 2.3. Main Results -- 3. Proof of Theorem 2.1 -- 3.1. Weak Form of the Integral Equation -- 3.2. Regularity in x -- 3.3. Regularity in t and the Pressure -- 4. Proof of Theorem 2.2 -- 4.1. Reduction to the Whole Space Problem -- 4.2. Integral Equation for the Whole Space Problem -- 4.3. Reconstruction Procedure -- References.
Record Nr. UNISA-996499865603316
Cham, Switzerland : , : Birkhäuser, , [2023]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Foundations of Geometric Continuum Mechanics : Geometry and Duality in Continuum Mechanics / / by Reuven Segev
Foundations of Geometric Continuum Mechanics : Geometry and Duality in Continuum Mechanics / / by Reuven Segev
Autore Segev Reuven
Edizione [1st ed. 2023.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2023
Descrizione fisica 1 online resource (410 pages)
Disciplina 531.7
Collana Advances in Continuum Mechanics
Soggetto topico Geometry, Differential
Continuum mechanics
Differential Geometry
Continuum Mechanics
Mecànica dels medis continus
Matemàtica
Soggetto genere / forma Llibres electrònics
ISBN 3-031-35655-1
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1. Introduction -- 2. Prelude: Finite Dimensional Systems -- Part I Algebraic Theory: Uniform Fluxes -- 3. Simplices in Affine Spaces and Their Boundaries -- 4. Uniform Fluxes in Affine Spaces -- 5. From Uniform Fluxes to Exterior Algebra -- Part II: Smooth Theory -- 6. Smooth Analysis on Manifolds: A Short Review -- 7. Interlude: Smooth Distributions of Defects -- 8. Smooth Fluxes -- 9. Frames, Body Points, and Spacetime Structure -- 10. Stresses -- 11. Smooth Electromagnetism on Manifolds -- 12. The Elasticity Problem -- 13. Symmetry and Dynamics -- Part III Non-Smooth, Global Theories -- 14. Banachable Space of Sections of Vector Bundles over Compact Manifolds -- 15. Manifolds of Sections and Embeddings -- 16. The General Framework for Global Analytic Stress Theory -- 17. Dual Spaces Corresponding to Spaces of Differentiable Sections of a Vector Bundle: Localization of Sections and Functionals -- 18. de Rham Currents -- 19. Interlude: Singular Distributions of Defects in Bodies -- 20. Vector-Valued Currents -- 21. The Representation of Forces by Stresses and Hyperstresses -- 22. Simple Forces and Stresses -- 23. Whitney's Geometric Integration Theory and Non-Smooth Bodies -- 24. Optimal Fields and Load Capacity of Bodies -- Index.
Record Nr. UNINA-9910755074103321
Segev Reuven  
Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2023
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Level Set Methods for Fluid-Structure Interaction [[electronic resource] /] / by Georges-Henri Cottet, Emmanuel Maitre, Thomas Milcent
Level Set Methods for Fluid-Structure Interaction [[electronic resource] /] / by Georges-Henri Cottet, Emmanuel Maitre, Thomas Milcent
Autore Cottet Georges-Henri
Edizione [1st ed. 2022.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022
Descrizione fisica 1 online resource (203 pages)
Disciplina 624.171
Collana Applied Mathematical Sciences
Soggetto topico Mathematical models
Continuum mechanics
Numerical analysis
Mathematics - Data processing
Mathematical Modeling and Industrial Mathematics
Continuum Mechanics
Numerical Analysis
Computational Science and Engineering
Models matemàtics
Mecànica dels medis continus
Anàlisi numèrica
Soggetto genere / forma Llibres electrònics
ISBN 3-031-08659-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1. Level Set methods and Lagrangian interfaces -- 2. Mathematical tools for continuum mechanics -- 3. Interaction of an incompressible fluid with an elastic membrane -- 4. Immersed bodies : the case of elastic bodies -- 5. Immersed bodies : the case of rigid bodies -- 6. Interaction between bodies by the Level Set method -- 7. Appendix -- 8. References. .
Record Nr. UNISA-996490347003316
Cottet Georges-Henri  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Level Set Methods for Fluid-Structure Interaction / / by Georges-Henri Cottet, Emmanuel Maitre, Thomas Milcent
Level Set Methods for Fluid-Structure Interaction / / by Georges-Henri Cottet, Emmanuel Maitre, Thomas Milcent
Autore Cottet Georges-Henri
Edizione [1st ed. 2022.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022
Descrizione fisica 1 online resource (203 pages)
Disciplina 624.171
Collana Applied Mathematical Sciences
Soggetto topico Mathematical models
Continuum mechanics
Numerical analysis
Mathematics - Data processing
Mathematical Modeling and Industrial Mathematics
Continuum Mechanics
Numerical Analysis
Computational Science and Engineering
Models matemàtics
Mecànica dels medis continus
Anàlisi numèrica
Soggetto genere / forma Llibres electrònics
ISBN 3-031-08659-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1. Level Set methods and Lagrangian interfaces -- 2. Mathematical tools for continuum mechanics -- 3. Interaction of an incompressible fluid with an elastic membrane -- 4. Immersed bodies : the case of elastic bodies -- 5. Immersed bodies : the case of rigid bodies -- 6. Interaction between bodies by the Level Set method -- 7. Appendix -- 8. References. .
Record Nr. UNINA-9910592989903321
Cottet Georges-Henri  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Mathematical applications in continuum and structural mechanics / / Francesco Marmo [and three others]
Mathematical applications in continuum and structural mechanics / / Francesco Marmo [and three others]
Pubbl/distr/stampa Cham, Switzerland : , : Springer International Publishing, , [2021]
Descrizione fisica 1 online resource (275 pages)
Disciplina 531
Collana Advanced Structured Materials
Soggetto topico Continuum mechanics - Mathematical models
Structural analysis (Engineering) - Mathematical models
Mecànica dels medis continus
Teoria de les estructures
Models matemàtics
Soggetto genere / forma Llibres electrònics
ISBN 3-030-42707-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Contents -- Contributors -- 1 Usage of Guided Wave Resonance Phenomena for Defect Detection in Laminate Elastic Structures -- 1.1 Introduction -- 1.2 Computational Models -- 1.3 Experimental Evaluation of Resonance Frequencies -- 1.4 Estimation of the Defect Size -- 1.5 Conclusion -- References -- 2 Modelling of Piezocomposites with Mechanical Interface Effects -- 2.1 Introduction -- 2.2 Effective Moduli Method for Homogenization of Two-Phase Piezoelectric Nanocomposite -- 2.3 Dimensionless Homogenization Problem -- 2.4 Finite Element Modelling -- 2.5 Modelling of Representative Volume Elements -- 2.6 Results and Discussion -- 2.7 Conclusion -- References -- 3 A Mathematical Model for Bone Cell Population Dynamics of Fracture Healing Considering the Effect of Energy Dissipation -- 3.1 Introduction -- 3.2 The Model -- 3.2.1 The Main Assumptions -- 3.2.2 The Governing Equations -- 3.2.3 The Stimulus -- 3.2.4 The Function κ() -- 3.2.5 The Mechanical Framework -- 3.2.6 Numerical Data -- 3.2.7 Healing of Bone -- 3.2.8 Dissipation -- 3.3 Results and Discussion -- 3.4 Conclusion -- References -- 4 Second Gradient Linear and Nonlinear Constitutive Models of Architectured Materials: Static and Dynamic Behaviors -- 4.1 Introduction -- 4.2 First- and Second-Order Effective Moduli of Periodic Networks -- 4.2.1 Analytical Method -- 4.2.2 Homogenized Viscoelastic Behavior -- 4.2.3 Incremental Scheme -- 4.3 Wave Propagation Analysis Based on Nonlinear Models -- 4.3.1 Strain Energy Density -- 4.4 Conclusion -- References -- 5 An Application of Coulomb-Friction Model to Predict Internal Dissipation in Concrete -- 5.1 Introduction -- 5.2 A Brief Synopsis of the Employed Model -- 5.2.1 3D Formulation of a Micromorphic Concrete-Based Material -- 5.2.2 Simplified Formulation for the Case of a Pure Compression -- 5.3 Numerical Simulations and Discussions.
5.4 Conclusion -- References -- 6 From the Swarm Robotics to Material Deformations -- 6.1 Introduction -- 6.2 Other Models in Literature -- 6.2.1 Position-Based Dynamics (PBD) -- 6.2.2 Swarm Robotics -- 6.3 The Model Here Proposed -- 6.3.1 A Recall About Graph Theory -- 6.3.2 Constructing the Model -- 6.3.3 Relationship with Other Models -- 6.3.4 Meaning of Neighbors -- 6.4 Numerical Simulations -- 6.4.1 Standard Simulations -- 6.4.2 Second Neighborhoods and Exotic Simulations -- 6.5 Conclusion -- References -- 7 A Review of the Class of Bouc-Wen Differential Models for Simulating Mechanical Hysteresis Phenomena -- 7.1 Introduction -- 7.2 Modeling of Symmetric Hysteresis Loops -- 7.2.1 Bouc Model and Its Modified Versions -- 7.2.2 Sensitivity Analysis -- 7.3 Modeling of Asymmetric Hysteresis Loops -- 7.3.1 Asymmetric Bouc-Wen Models -- 7.3.2 Sensitivity Analysis -- 7.4 Modeling of Pinched Hysteresis Loops -- 7.4.1 Pinching Bouc-Wen Models -- 7.4.2 Sensitivity Analysis -- 7.5 Modeling of Degrading Hysteresis Loops -- 7.5.1 Degrading Bouc-Wen Models -- 7.5.2 Sensitivity Analysis -- 7.6 Conclusion -- References -- 8 A Generalized Formulation of Time Integration Methods for Nonlinear Dynamic Analysis of Hysteretic Mechanical Systems -- 8.1 Introduction -- 8.2 Families of Time Integration Methods -- 8.2.1 Nonlinear Equilibrium Equations -- 8.2.2 Generalized Formulation of Time Integration Methods -- 8.3 Conventional Time Integration Methods -- 8.3.1 Newmark's Family of Methods -- 8.3.2 Some Instances of the NFMs -- 8.3.3 Implementation Scheme of the NFMs -- 8.4 Structure-Dependent Time Integration Methods -- 8.4.1 Chang's Family of Explicit Methods -- 8.4.2 Some Instances of the CFEMs -- 8.4.3 Implementation Scheme of the CFEMs -- 8.5 Numerical Experiments -- 8.5.1 Mechanical System Properties -- 8.5.2 Applied Generalized External Force.
8.5.3 Hysteretic Model Parameters -- 8.5.4 Results of the Nonlinear Time History Analyses -- 8.6 Conclusion -- References -- 9 Quasi-Harmonic Solutions for Transversely Isotropic Magneto-Electro-Thermo-Elasticity: A Symbolic Mathematics Approach -- 9.1 Introduction -- 9.2 Field Equations -- 9.3 A General Solution to the Field Equations in Terms of Quasi-Harmonic Potentials -- 9.3.1 Inversion of the Differential Operator mathcalL -- 9.3.2 Factorization of the Differential Equation |mathcalL|= 0 -- 9.4 Automatic Evaluation of |mathcalL| and mathcalL* and Relevant Coefficients -- 9.4.1 Evaluation of |mathcalL| -- 9.4.2 Evaluation of mathcalL* -- 9.5 Conclusion -- References -- 10 Mathematical Tools for the Seismic Analysis of Reinforced Concrete Structures: A Selected Review -- 10.1 Introduction -- 10.2 Review of Strategies Accounting for Global Torsion in Buildings -- 10.2.1 Review of the Dynamic Equivalent Rotational Spectrum -- 10.3 Computation of Multicomponent Actions by Seismic Envelopes -- 10.4 Capacity Checks of Reinforced Concrete Beams -- 10.4.1 A General Algorithm to Perform Capacity Checks by the Supreme Envelope -- 10.5 Conclusions -- References -- 11 Form Finding of Shell Structures by Using Membrane Theory -- 11.1 Introduction -- 11.2 The Membrane Theory of Shells -- 11.2.1 Global and Local Reference Frames -- 11.2.2 Transformation Formulas for Lengths and Areas -- 11.2.3 Distributed Loads and Stress Components -- 11.2.4 Equilibrium -- 11.3 Form-Finding Algorithm -- 11.3.1 Discretization of the Equilibrium Equations by the Finite Difference Method -- 11.3.2 Assigning the Distribution of Projected Membrane Stresses -- 11.3.3 Evaluation of the Shell Mid-Surface Height -- 11.3.4 Iterative Procedure for Assigning Projected Loads -- 11.4 Numerical Examples -- 11.4.1 Shell with One Free Side -- 11.4.2 Shell Supported at Corners.
11.5 Conclusion -- References -- 12 Influence of Non-structural Components on Equivalent Linearization of Buildings -- 12.1 Introduction -- 12.2 Brief Review of Tail-Equivalent Linearization -- 12.3 Influence of Secondary Devices on TELS -- 12.3.1 Frequency Content Comparison -- 12.3.2 First Excursion Probability Comparison -- 12.4 Conclusion -- References -- 13 Do We Really Need Pantographic Structures? -- 13.1 Introduction -- 13.2 Metamaterials Are (Natural) Materials on Demand -- 13.3 Second Gradient Theories -- 13.4 Microstructure in Continuum Mechanics -- 13.4.1 The Synthesis Problem -- 13.5 Why We Really Need Pantographic Structures -- 13.5.1 The Existence of Pantographic Metamaterial Motivates the Need of Second Gradient Theories -- 13.5.2 A Mechanical Diode -- 13.5.3 An Iterative Algorithm for Synthesising Metamaterials -- 13.6 Conclusion -- References.
Record Nr. UNISA-996466559903316
Cham, Switzerland : , : Springer International Publishing, , [2021]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Mathematical applications in continuum and structural mechanics / / Francesco Marmo [and three others]
Mathematical applications in continuum and structural mechanics / / Francesco Marmo [and three others]
Pubbl/distr/stampa Cham, Switzerland : , : Springer International Publishing, , [2021]
Descrizione fisica 1 online resource (275 pages)
Disciplina 531
Collana Advanced Structured Materials
Soggetto topico Continuum mechanics - Mathematical models
Structural analysis (Engineering) - Mathematical models
Mecànica dels medis continus
Teoria de les estructures
Models matemàtics
Soggetto genere / forma Llibres electrònics
ISBN 3-030-42707-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Contents -- Contributors -- 1 Usage of Guided Wave Resonance Phenomena for Defect Detection in Laminate Elastic Structures -- 1.1 Introduction -- 1.2 Computational Models -- 1.3 Experimental Evaluation of Resonance Frequencies -- 1.4 Estimation of the Defect Size -- 1.5 Conclusion -- References -- 2 Modelling of Piezocomposites with Mechanical Interface Effects -- 2.1 Introduction -- 2.2 Effective Moduli Method for Homogenization of Two-Phase Piezoelectric Nanocomposite -- 2.3 Dimensionless Homogenization Problem -- 2.4 Finite Element Modelling -- 2.5 Modelling of Representative Volume Elements -- 2.6 Results and Discussion -- 2.7 Conclusion -- References -- 3 A Mathematical Model for Bone Cell Population Dynamics of Fracture Healing Considering the Effect of Energy Dissipation -- 3.1 Introduction -- 3.2 The Model -- 3.2.1 The Main Assumptions -- 3.2.2 The Governing Equations -- 3.2.3 The Stimulus -- 3.2.4 The Function κ() -- 3.2.5 The Mechanical Framework -- 3.2.6 Numerical Data -- 3.2.7 Healing of Bone -- 3.2.8 Dissipation -- 3.3 Results and Discussion -- 3.4 Conclusion -- References -- 4 Second Gradient Linear and Nonlinear Constitutive Models of Architectured Materials: Static and Dynamic Behaviors -- 4.1 Introduction -- 4.2 First- and Second-Order Effective Moduli of Periodic Networks -- 4.2.1 Analytical Method -- 4.2.2 Homogenized Viscoelastic Behavior -- 4.2.3 Incremental Scheme -- 4.3 Wave Propagation Analysis Based on Nonlinear Models -- 4.3.1 Strain Energy Density -- 4.4 Conclusion -- References -- 5 An Application of Coulomb-Friction Model to Predict Internal Dissipation in Concrete -- 5.1 Introduction -- 5.2 A Brief Synopsis of the Employed Model -- 5.2.1 3D Formulation of a Micromorphic Concrete-Based Material -- 5.2.2 Simplified Formulation for the Case of a Pure Compression -- 5.3 Numerical Simulations and Discussions.
5.4 Conclusion -- References -- 6 From the Swarm Robotics to Material Deformations -- 6.1 Introduction -- 6.2 Other Models in Literature -- 6.2.1 Position-Based Dynamics (PBD) -- 6.2.2 Swarm Robotics -- 6.3 The Model Here Proposed -- 6.3.1 A Recall About Graph Theory -- 6.3.2 Constructing the Model -- 6.3.3 Relationship with Other Models -- 6.3.4 Meaning of Neighbors -- 6.4 Numerical Simulations -- 6.4.1 Standard Simulations -- 6.4.2 Second Neighborhoods and Exotic Simulations -- 6.5 Conclusion -- References -- 7 A Review of the Class of Bouc-Wen Differential Models for Simulating Mechanical Hysteresis Phenomena -- 7.1 Introduction -- 7.2 Modeling of Symmetric Hysteresis Loops -- 7.2.1 Bouc Model and Its Modified Versions -- 7.2.2 Sensitivity Analysis -- 7.3 Modeling of Asymmetric Hysteresis Loops -- 7.3.1 Asymmetric Bouc-Wen Models -- 7.3.2 Sensitivity Analysis -- 7.4 Modeling of Pinched Hysteresis Loops -- 7.4.1 Pinching Bouc-Wen Models -- 7.4.2 Sensitivity Analysis -- 7.5 Modeling of Degrading Hysteresis Loops -- 7.5.1 Degrading Bouc-Wen Models -- 7.5.2 Sensitivity Analysis -- 7.6 Conclusion -- References -- 8 A Generalized Formulation of Time Integration Methods for Nonlinear Dynamic Analysis of Hysteretic Mechanical Systems -- 8.1 Introduction -- 8.2 Families of Time Integration Methods -- 8.2.1 Nonlinear Equilibrium Equations -- 8.2.2 Generalized Formulation of Time Integration Methods -- 8.3 Conventional Time Integration Methods -- 8.3.1 Newmark's Family of Methods -- 8.3.2 Some Instances of the NFMs -- 8.3.3 Implementation Scheme of the NFMs -- 8.4 Structure-Dependent Time Integration Methods -- 8.4.1 Chang's Family of Explicit Methods -- 8.4.2 Some Instances of the CFEMs -- 8.4.3 Implementation Scheme of the CFEMs -- 8.5 Numerical Experiments -- 8.5.1 Mechanical System Properties -- 8.5.2 Applied Generalized External Force.
8.5.3 Hysteretic Model Parameters -- 8.5.4 Results of the Nonlinear Time History Analyses -- 8.6 Conclusion -- References -- 9 Quasi-Harmonic Solutions for Transversely Isotropic Magneto-Electro-Thermo-Elasticity: A Symbolic Mathematics Approach -- 9.1 Introduction -- 9.2 Field Equations -- 9.3 A General Solution to the Field Equations in Terms of Quasi-Harmonic Potentials -- 9.3.1 Inversion of the Differential Operator mathcalL -- 9.3.2 Factorization of the Differential Equation |mathcalL|= 0 -- 9.4 Automatic Evaluation of |mathcalL| and mathcalL* and Relevant Coefficients -- 9.4.1 Evaluation of |mathcalL| -- 9.4.2 Evaluation of mathcalL* -- 9.5 Conclusion -- References -- 10 Mathematical Tools for the Seismic Analysis of Reinforced Concrete Structures: A Selected Review -- 10.1 Introduction -- 10.2 Review of Strategies Accounting for Global Torsion in Buildings -- 10.2.1 Review of the Dynamic Equivalent Rotational Spectrum -- 10.3 Computation of Multicomponent Actions by Seismic Envelopes -- 10.4 Capacity Checks of Reinforced Concrete Beams -- 10.4.1 A General Algorithm to Perform Capacity Checks by the Supreme Envelope -- 10.5 Conclusions -- References -- 11 Form Finding of Shell Structures by Using Membrane Theory -- 11.1 Introduction -- 11.2 The Membrane Theory of Shells -- 11.2.1 Global and Local Reference Frames -- 11.2.2 Transformation Formulas for Lengths and Areas -- 11.2.3 Distributed Loads and Stress Components -- 11.2.4 Equilibrium -- 11.3 Form-Finding Algorithm -- 11.3.1 Discretization of the Equilibrium Equations by the Finite Difference Method -- 11.3.2 Assigning the Distribution of Projected Membrane Stresses -- 11.3.3 Evaluation of the Shell Mid-Surface Height -- 11.3.4 Iterative Procedure for Assigning Projected Loads -- 11.4 Numerical Examples -- 11.4.1 Shell with One Free Side -- 11.4.2 Shell Supported at Corners.
11.5 Conclusion -- References -- 12 Influence of Non-structural Components on Equivalent Linearization of Buildings -- 12.1 Introduction -- 12.2 Brief Review of Tail-Equivalent Linearization -- 12.3 Influence of Secondary Devices on TELS -- 12.3.1 Frequency Content Comparison -- 12.3.2 First Excursion Probability Comparison -- 12.4 Conclusion -- References -- 13 Do We Really Need Pantographic Structures? -- 13.1 Introduction -- 13.2 Metamaterials Are (Natural) Materials on Demand -- 13.3 Second Gradient Theories -- 13.4 Microstructure in Continuum Mechanics -- 13.4.1 The Synthesis Problem -- 13.5 Why We Really Need Pantographic Structures -- 13.5.1 The Existence of Pantographic Metamaterial Motivates the Need of Second Gradient Theories -- 13.5.2 A Mechanical Diode -- 13.5.3 An Iterative Algorithm for Synthesising Metamaterials -- 13.6 Conclusion -- References.
Record Nr. UNINA-9910510535503321
Cham, Switzerland : , : Springer International Publishing, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Thermodynamics of materials with memory : theory and applications / / Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
Thermodynamics of materials with memory : theory and applications / / Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
Autore Amendola Giovambattista
Edizione [Second edition.]
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
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
ISBN 3-030-80534-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
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.
Record Nr. UNINA-9910506381203321
Amendola Giovambattista  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Thermodynamics of materials with memory : theory and applications / / Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
Thermodynamics of materials with memory : theory and applications / / Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
Autore Amendola Giovambattista
Edizione [Second edition.]
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
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
ISBN 3-030-80534-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
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.
Record Nr. UNISA-996466398203316
Amendola Giovambattista  
Cham, Switzerland : , : Springer, , [2021]
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