Thermodynamics of Materials with Memory: Theory and Applications

By Joel S. Miller

Part I: Continuum Mechanics and Classical Materials.- Introduction to Continuum Mechanics.- Materials with Constitutive Equations That Are Local in Time.- Part II: Continuum Thermodynamics and Constitutive Equations of Mechanics and Electromagnetism.- Principles of Thermodynamics.- Free Energies and the Dissipation Principle.- Thermodynamics of Materials with Memory.- Thermoelectromagnetism of Continuous Media.- Part III: Free Energies for Materials with Linear 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.- Free Energies for the Case of Isolated Singularites.- Constructing Free Energies for Materials with Memory.- Minimal States and Periodic Histories.- Second Order Approximation for Heat Conduction: Dissipation Principle and Free Energies.- Free Energies for Nonlinear Materials with Memory.- Free Energies for Nonlocal Materials.- The Minimum and Related Free Energies for Dielectric Materials.- Fractional Derivative Models of Materials with Memory.- Part IV: The Dynamical Equations for Materials with Memory.- 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.- Conventions and Some Properties of Vector Spaces.- Some Properties of Function on the Complex Plane.- Fourier Transformations.

• Format: Paperback
• Language: English
• ISBN: 3030805360
• ISBN13: 9783030805364
• Release Date: October 2022
• Publisher: Springer
• Length: 755 Pages
• Weight: 2.36 lbs.
• Dimensions: 1.6" x 6.1" x 9.2"