Thermodynamics of Materials with Memory

Beschreibung

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.
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.

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

Autor*in

Giovambattista Amendola

Themen in »Thermodynamics of Materials with Memory«

Continuum Thermodynamics Dynamical equations Fading memory Free energy Minimal state

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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)

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