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Thermodynamics of Materials with Memory

Theory and Applications

  • Book
  • © 2012

Overview

Authors:
  1. Giovambattista Amendola

    1. , Dipartimento di Matematica Applicata "U., University of Pisa, Pisa, Italy

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  2. Mauro Fabrizio

    1. , Dipartimento di Matematica,, University of Bologna, Bologna, Italy

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    You can also search for this author in PubMed   Google Scholar

  3. John Murrough Golden

    1. , School of Mathematical Sciences, Dublin Institute of Technology, Dublin, Ireland

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  • 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
  • Includes supplementary material: sn.pub/extras

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Table of contents (25 chapters)

  1. Front Matter

    Pages i-xv
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  2. Introduction

    • Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
    Pages 1-3

  3. Continuum Mechanics and Classical Materials

    1. Front Matter

      Pages 5-5
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    2. Introduction to Continuum Mechanics

      • Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 7-42

    3. Materials with Constitutive Equations That Are Local in Time

      • Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 43-72

  4. Continuum Thermodynamics and Constitutive Equations

    1. Front Matter

      Pages 73-73
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    2. Principles of Thermodynamics

      • Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 75-98

    3. Free Energies and the Dissipation Principle

      • Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 99-108

    4. Thermodynamics of Materials with Memory

      • Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 109-122

  5. Free Energies for Materials with Linear Memory

    1. Front Matter

      Pages 123-123
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    2. A Linear Memory Model

      • Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 125-154

    3. Viscoelastic Solids and Fluids

      • Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 155-198

    4. Heat Conductors

      • Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 199-216

    5. Free Energies on Special Classes of Material

      • Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 217-234

    6. The Minimum Free Energy

      • Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 235-267

    7. Representation of the Minimum Free Energy in the Time Domain

      • Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 269-276

    8. Minimum Free Energy for Viscoelastic Solids, Fluids, and Heat Conductors

      • Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 277-305

    9. The Minimum Free Energy for a Continuous-Spectrum Material

      • Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 307-323

    10. The Minimum Free Energy for a Finite-Memory Material

      • Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 325-334

    11. A Family of Free Energies

      • Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 335-355
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Keywords

About this book

This is a work in four parts, dealing with the mechanics and thermodynamics of materials with memory, including properties of the dynamical equations which describe their evolution in time under varying loads. The first part is an introduction to Continuum Mechanics with sections dealing with classical Fluid Mechanics and Elasticity, linear and non-linear. The second part is devoted to Continuum Thermodynamics, which is used to derive constitutive equations of materials with memory, including viscoelastic solids, fluids, heat conductors and some examples of non-simple materials. In part three, free energies for materials with linear memory constitutive relations are comprehensively explored. The new concept of a minimal state is also introduced. Formulae derived over the last decade for the minimum and related free energies are discussed in depth. Also, a new single integral free energy which is a functional of the minimal state is analyzed in detail. Finally, free energies for examples of non-simple materials are considered. In the final part, existence, uniqueness and stability results are presented for the integrodifferential equations describing the dynamical evolution of viscoelastic materials. A new approach to these topics, based on the use of minimal states rather than histories, is discussed in detail. 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.

Reviews

From the reviews:

“Modern technology has evolved many material properties leading to memory for which a unifying description seems impossible. The book under review attempts to provide such a unifying description. It presents detailed accounts on the mechanics and thermodynamics of materials with memory, including properties of the dynamical equations which describe their evolution in time under varying loads. … The book presents a wealth of information on materials with memory and it will attract a wide readership from academia.” (K. N. Shukla, Zentralblatt MATH, Vol. 1237, 2012)

Authors and Affiliations

  • , Dipartimento di Matematica Applicata "U., University of Pisa, Pisa, Italy

    Giovambattista Amendola

  • , Dipartimento di Matematica,, University of Bologna, Bologna, Italy

    Mauro Fabrizio

  • , School of Mathematical Sciences, Dublin Institute of Technology, Dublin, Ireland

    John Murrough Golden

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