Thermodynamics of materials with memory : theory and applications / Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden.
Amendola, Giovambattista, author.; Fabrizio, Mauro, 1940- author.; Golden, J. M. (John M.), 1945- author.
2021
QC311
Available Online

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Title Thermodynamics of materials with memory : theory and applications / Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden.
Author Amendola, Giovambattista, author.
Edition Second edition.
ISBN 9783030805340 (electronic bk.)
3030805344 (electronic bk.)
9783030805333 (print)
DOI https://doi.org/10.1007/978-3-030-80534-0
Published Cham, Switzerland : Springer, 2021.
Language English
Description 1 online resource (xxi, 755 pages) : illustrations
Item Number 10.1007/978-3-030-80534-0 doi
Call Number QC311
Dewey Decimal Classification 536/.7
Summary 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Digital File Characteristics text file
PDF
Source of Description Online resource; title from PDF title page (SpringerLink, viewed November 1, 2021).
Added Author Fabrizio, Mauro, 1940- author.
Golden, J. M. (John M.), 1945- author.
Available in Other Form Print version: 9783030805333
Print version: 9783030805357
Print version: 9783030805364
Linked Resources Online Access
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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.

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