Overview
- This is the first comprehensive treatment in book form of free energies of materials with memory
- This is the first systematic presentation in book form of a new method of analysis of the evolution equations of viscoelastic materials, using the concept of a minimal state
- The various new topics included are firmly rooted on a foundation of Continuum Thermodynamics, which is discussed in detail, including a general abstract formulation of the theory
- Constraints imposed by thermodynamics are extensively used
- The work is self-contained to a significant degree in that it contains a detailed presentation of Continuum Mechanics and classical theories
- This is the first systematic treatment in book for of the Saint Venant
- Problem for viscoelastic materials and of the controllibility of thermoelastic systems with memory
- Contains new topics in free energy functionals and fractional derivative models
- Examines explicit forms of free energies in modelling the behavior of material elements
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About this book
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.
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.
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Keywords
- Continuum Thermodynamics
- Thermoelectromagnetism
- Fading memory
- Free energy
- Minimal state
- Nonlocal materials
- Fractional derivative models
- Dynamical equations
- Initial and boundary value problems
- Existence, uniqueness, stability
- Control theory
- Inverse problems
- Saint Venant problems with memory
- Asymptotic behavior
Table of contents (30 chapters)
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Front Matter
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Continuum Mechanics and Classical Materials
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Front Matter
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Continuum Thermodynamics and Constitutive Equations of Mechanics and Electromagnetism
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Front Matter
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Free Energies for Materials with Linear Memory
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Front Matter
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Authors and Affiliations
Bibliographic Information
Book Title: Thermodynamics of Materials with Memory
Book Subtitle: Theory and Applications
Authors: Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
DOI: https://doi.org/10.1007/978-3-030-80534-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-80533-3Published: 21 October 2021
Softcover ISBN: 978-3-030-80536-4Published: 22 October 2022
eBook ISBN: 978-3-030-80534-0Published: 20 October 2021
Edition Number: 2
Number of Pages: XXI, 755
Number of Illustrations: 11 b/w illustrations
Topics: Mathematical Applications in the Physical Sciences, Characterization and Evaluation of Materials, Solid Mechanics, Classical Mechanics