Thermodynamics of Materials with Memory

Theory and Applications

  • Giovambattista Amendola
  • Mauro Fabrizio
  • John Murrough Golden

Table of contents

  1. Front Matter
    Pages i-xv
  2. Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
    Pages 1-3
  3. Continuum Mechanics and Classical Materials

    1. Front Matter
      Pages 5-5
    2. Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 7-42
    3. Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 43-72
  4. Continuum Thermodynamics and Constitutive Equations

    1. Front Matter
      Pages 73-73
    2. Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 75-98
    3. Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 99-108
    4. Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 109-122
  5. Free Energies for Materials with Linear Memory

    1. Front Matter
      Pages 123-123
    2. Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 125-154
    3. Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 155-198
    4. Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 199-216
    5. Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 217-234
    6. Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 235-267
    7. Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 269-276
    8. Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 277-305
    9. Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 307-323
    10. Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 325-334
    11. Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
      Pages 335-355

About this book

Introduction

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.

Keywords

Continuum Thermodynamics Dynamical equations Fading memory Free energy Minimal state

Authors and affiliations

  • Giovambattista Amendola
    • 1
  • Mauro Fabrizio
    • 2
  • John Murrough Golden
    • 3
  1. 1., Dipartimento di Matematica Applicata "U.University of PisaPisaItaly
  2. 2., Dipartimento di Matematica,University of BolognaBolognaItaly
  3. 3., School of Mathematical SciencesDublin Institute of TechnologyDublinIreland

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-1692-0
  • Copyright Information Springer Science+Business Media, LLC 2012
  • Publisher Name Springer, Boston, MA
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-1691-3
  • Online ISBN 978-1-4614-1692-0
  • About this book