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Thermodynamics of materials with memory = theory and applications /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Thermodynamics of materials with memory/ by Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden.
Reminder of title:	theory and applications /
Author:	Amendola, Giovambattista.
other author:	Fabrizio, Mauro.
Published:	Cham :Springer International Publishing : : 2021.,
Description:	xxi, 755 p. :ill., digital ;24 cm.
[NT 15003449]:	Part I: Continuum Mechanics and Classical Materials -- Introduction to Continuum Mechanics -- Materials with Constitutive Equations That Are Local in Time -- Part II: Continuum Thermodynamics and Constitutive Equations of Mechanics and Electromagnetism -- Principles of Thermodynamics -- Free Energies and the Dissipation Principle -- Thermodynamics of Materials with Memory -- Thermoelectromagnetism of Continuous Media -- Part III: Free Energies for Materials with Linear Memory -- A Linear Memory Model -- Viscoelastic Solids and Fluids -- Heat Conductors -- Free Energies on Special Classes of Material -- The Minimum Free Energy -- Representation of the Minimum Free Energy in the Time Domain -- Minimum Free Energy for Viscoelastic Solids, Fluids, and Heat Conductors -- The Minimum Free Energy for a Continuous-Spectrum Material -- The Minimum Free Energy for a Finite-Memory Material -- Free Energies for the Case of Isolated Singularites -- Constructing Free Energies for Materials with Memory -- Minimal States and Periodic Histories -- Second Order Approximation for Heat Conduction: Dissipation Principle and Free Energies -- Free Energies for Nonlinear Materials with Memory -- Free Energies for Nonlocal Materials -- The Minimum and Related Free Energies for Dielectric Materials -- Fractional Derivative Models of Materials with Memory -- Part IV: The Dynamical Equations for Materials with Memory -- Existence and Uniqueness -- Controllability of Thermoelastic Systems with Memory -- The Saint-Venant Problem for Viscoelastic Materials -- Exponential Decay -- Semigroup Theory for Abstract Equations with Memory -- Identification Problems for Integrodifferential Equations -- Dynamics of Viscoelastic Fluids -- Conventions and Some Properties of Vector Spaces -- Some Properties of Function on the Complex Plane -- Fourier Transformations.
Contained By:	Springer Nature eBook
Subject:	Thermodynamics - Mathematical models. -
Online resource:	https://doi.org/10.1007/978-3-030-80534-0
ISBN:	9783030805340

Thermodynamics of materials with memory = theory and applications /
Amendola, Giovambattista.

Thermodynamics of materials with memorytheory and applications /[electronic resource] :by Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden. - Second edition. - Cham :Springer International Publishing :2021. - xxi, 755 p. :ill., digital ;24 cm.

Part I: Continuum Mechanics and Classical Materials -- Introduction to Continuum Mechanics -- Materials with Constitutive Equations That Are Local in Time -- Part II: Continuum Thermodynamics and Constitutive Equations of Mechanics and Electromagnetism -- Principles of Thermodynamics -- Free Energies and the Dissipation Principle -- Thermodynamics of Materials with Memory -- Thermoelectromagnetism of Continuous Media -- Part III: Free Energies for Materials with Linear Memory -- A Linear Memory Model -- Viscoelastic Solids and Fluids -- Heat Conductors -- Free Energies on Special Classes of Material -- The Minimum Free Energy -- Representation of the Minimum Free Energy in the Time Domain -- Minimum Free Energy for Viscoelastic Solids, Fluids, and Heat Conductors -- The Minimum Free Energy for a Continuous-Spectrum Material -- The Minimum Free Energy for a Finite-Memory Material -- Free Energies for the Case of Isolated Singularites -- Constructing Free Energies for Materials with Memory -- Minimal States and Periodic Histories -- Second Order Approximation for Heat Conduction: Dissipation Principle and Free Energies -- Free Energies for Nonlinear Materials with Memory -- Free Energies for Nonlocal Materials -- The Minimum and Related Free Energies for Dielectric Materials -- Fractional Derivative Models of Materials with Memory -- Part IV: The Dynamical Equations for Materials with Memory -- Existence and Uniqueness -- Controllability of Thermoelastic Systems with Memory -- The Saint-Venant Problem for Viscoelastic Materials -- Exponential Decay -- Semigroup Theory for Abstract Equations with Memory -- Identification Problems for Integrodifferential Equations -- Dynamics of Viscoelastic Fluids -- Conventions and Some Properties of Vector Spaces -- Some Properties of Function on the Complex Plane -- Fourier Transformations.

This monograph deals with the mechanics and thermodynamics of materials with memory, including properties of the dynamical equations that describe their evolution in time under varying loads. A work in four parts, the first is an introduction to continuum mechanics, including classical fluid mechanics, linear and non-linear elasticity. The second part considers continuum thermodynamics and its use to derive constitutive equations of materials with memory, including viscoelastic solids, fluids, heat conductors and some examples of non-simple materials. In the third part, free energies for materials with linear memory constitutive relations are discussed. The concept of a minimal state is introduced. Explicit formulae are presented for the minimum and related free energies. The final part deals with existence, uniqueness, and stability results for the integrodifferential equations describing the dynamical evolution of viscoelastic materials, including a new approach based on minimal states rather than histories. There are also chapters on the controllability of thermoelastic systems with memory, the Saint-Venant problem for viscoelastic materials and on the theory of inverse problems. The second edition includes a new chapter on thermoelectromagnetism as well as recent findings on minimal states and free energies. It considers the case of minimum free energies for non-simple materials and dielectrics, together with an introduction to fractional derivative models.

ISBN: 9783030805340

Standard No.: 10.1007/978-3-030-80534-0doiSubjects--Topical Terms:

653842
Thermodynamics
--Mathematical models.

LC Class. No.: QC311 / .A54 2021

Dewey Class. No.: 536.7

Thermodynamics of materials with memory = theory and applications /
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245 1 0 $a Thermodynamics of materials with memory $h [electronic resource] : $b theory and applications / $c by Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden.
250 $a Second edition.
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300 $a xxi, 755 p. : $b ill., digital ; $c 24 cm.
505 0 $a Part I: Continuum Mechanics and Classical Materials -- Introduction to Continuum Mechanics -- Materials with Constitutive Equations That Are Local in Time -- Part II: Continuum Thermodynamics and Constitutive Equations of Mechanics and Electromagnetism -- Principles of Thermodynamics -- Free Energies and the Dissipation Principle -- Thermodynamics of Materials with Memory -- Thermoelectromagnetism of Continuous Media -- Part III: Free Energies for Materials with Linear Memory -- A Linear Memory Model -- Viscoelastic Solids and Fluids -- Heat Conductors -- Free Energies on Special Classes of Material -- The Minimum Free Energy -- Representation of the Minimum Free Energy in the Time Domain -- Minimum Free Energy for Viscoelastic Solids, Fluids, and Heat Conductors -- The Minimum Free Energy for a Continuous-Spectrum Material -- The Minimum Free Energy for a Finite-Memory Material -- Free Energies for the Case of Isolated Singularites -- Constructing Free Energies for Materials with Memory -- Minimal States and Periodic Histories -- Second Order Approximation for Heat Conduction: Dissipation Principle and Free Energies -- Free Energies for Nonlinear Materials with Memory -- Free Energies for Nonlocal Materials -- The Minimum and Related Free Energies for Dielectric Materials -- Fractional Derivative Models of Materials with Memory -- Part IV: The Dynamical Equations for Materials with Memory -- Existence and Uniqueness -- Controllability of Thermoelastic Systems with Memory -- The Saint-Venant Problem for Viscoelastic Materials -- Exponential Decay -- Semigroup Theory for Abstract Equations with Memory -- Identification Problems for Integrodifferential Equations -- Dynamics of Viscoelastic Fluids -- Conventions and Some Properties of Vector Spaces -- Some Properties of Function on the Complex Plane -- Fourier Transformations.
520 $a This monograph deals with the mechanics and thermodynamics of materials with memory, including properties of the dynamical equations that describe their evolution in time under varying loads. A work in four parts, the first is an introduction to continuum mechanics, including classical fluid mechanics, linear and non-linear elasticity. The second part considers continuum thermodynamics and its use to derive constitutive equations of materials with memory, including viscoelastic solids, fluids, heat conductors and some examples of non-simple materials. In the third part, free energies for materials with linear memory constitutive relations are discussed. The concept of a minimal state is introduced. Explicit formulae are presented for the minimum and related free energies. The final part deals with existence, uniqueness, and stability results for the integrodifferential equations describing the dynamical evolution of viscoelastic materials, including a new approach based on minimal states rather than histories. There are also chapters on the controllability of thermoelastic systems with memory, the Saint-Venant problem for viscoelastic materials and on the theory of inverse problems. The second edition includes a new chapter on thermoelectromagnetism as well as recent findings on minimal states and free energies. It considers the case of minimum free energies for non-simple materials and dielectrics, together with an introduction to fractional derivative models.
650 0 $a Thermodynamics $x Mathematical models. $3 653842
650 0 $a Smart materials $x Mathematical models. $3 904964
650 0 $a Continuum mechanics. $3 535472
650 1 4 $a Mathematical Applications in the Physical Sciences. $3 1566152
650 2 4 $a Characterization and Evaluation of Materials. $3 890988
650 2 4 $a Solid Mechanics. $3 3381524
650 2 4 $a Classical Mechanics. $3 3216970
700 1 $a Fabrizio, Mauro. $3 1566716
700 1 $a Golden, J. M. $q (John M.) $3 3522304
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773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-3-030-80534-0
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