Overview

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.

Full Product Details

Author:   Giovambattista Amendola ,  Mauro Fabrizio ,  John Murrough Golden
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2012
Dimensions:   Width: 15.50cm , Height: 3.10cm , Length: 23.50cm
Weight:   1.045kg
ISBN:  

9781461416913

ISBN 10:   1461416914
Pages:   576
Publication Date:   17 November 2011
Audience:   Professional and scholarly ,  Professional & Vocational
Replaced By:   9783030805333
Format:   Hardback
Publisher's Status:   Active
Availability:   Awaiting stock  
The supplier is currently out of stock of this item. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out for you.

Table of Contents

Introduction to Continuum.-Materials with Constitutive Equations That Are Local in Time.- Principles of Thermodynamics.- Free Energies and the Dissipation Principle.-Thermodynamics of Materials with 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.- A Family of Free Energies.- Properties and Explicit Forms of Free Energies for the Case of Isolated Singularities.- Free Energies for Nonlocal Materials.- 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.- A Conventions and Some Properties of Vector Spaces.- References.- Index.

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)

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)

Author Information

Tab Content 6

Author Website:  

Countries Available

All regions