Maugin G.A. The Thermomechanics of Nonlinear Irreversible Behaviours: An Introduction

Simgapore: World Scientific, 1999. — 385 p.In this invaluable book, macroscopic irreversible thermodynamics is presented in its realm and its splendor by appealing to the notion of internal variables of state. This applies to both fluids and solids with or without microstructures of mechanical or electromagnetic origin. This unmatched richness of essentially nonlinear behaviors is the result of the use of modern mathematical techniques such as convex analysis in a clear-cut framework which allows one to put under the umbrella of “irreversible thermodynamics” behaviors which until now have been commonly considered either not easily covered, or even impossible to incorporate into such a framework.The book is intended for all students and researchers whose main concern is the rational modeling of complex and/or new materials with physical and engineering applications, such as those accounting for coupled-field, hysteresis, fracture, nonlinear-diffusion, and phase-transformation phenomena.ForewordIntrduction: A post-Duhemian thermodynamicsThermostatics and ThermodynamicsThermodynamic Systems
Thermodynamic States
Thermostatics (Born-Caratheodory)
Axioms of Thermostatics
Scaling of Temperature, Carnot's Theorem
Thermodynamic Potentials
The Evolution of Real Systems; ContinuaVarious Thermodynamics
Preliminary Remarks
Theory of Irreversible Processes (T.I.P.)
Axiom of Local State
Application to Deformable Material Continua
The Compressible Newtonian Fluid
The Linear Viscoelastic Solid
Finite-Strain Behavior of a Solid
Rubber-Like Materials
Anisotropic Elastic Materials
Onsager-Casimir Symmetry Relations
Dissipation PotentialRational ThermodynamicsGeneral Features
Thermoelastic Materials
Comparison with T.I.P.
Further Improvements
Extended Thermodynamics
Thermodynamics with Internal VariablesThermodynamics wthin Internal VariablesNature and Choice of Internal Variables
Internal Variables and Functional Constitutive Equations
Non-Equilibrium and Equilibrium States
Accompanying Processes and States
Verbal Statement of the L.A.S.
Formal Statement of the L.A.S.
Applying T.I.P. to T.I.V.
Potentials of Dissipation
Internal Variables and Microstructure
Highly Heterogeneous Bodies
Internal Variables or Internal Degrees of Freedom?
Internal Variables and Phase Transitions
Comparison with Extended ThermodynamicsApplications: General FrameworkConvexity of the Energy
General Properties of Dissipation Potentials
Convex Pseudo-Potential of Dissipation
Nonconvex Dissipation Potential
Reminder of Basic Equations
The Case Solids
The Case of FluidsViscosity in Complex FluidsIntroductory Remarks
The Notion of Simple (Non-Newtonian) Fluid
Statistical Theory of Polymeric Fluids
Molecular Models
Evolution Equation for the Conformation
Stress TensorThermodynamics with Internal VariablesGeneral View
The Internal Variable is an Anelastic Strain
The Internal Variable is a Conformation
The Internal Variable is a Vector
The Internal Variable is a Scalar
Forced Thermodynamic Systems
Diffusion and Migration
Vorticity and Conformation
Liquid Crystals
Structurally Complex Flows
ConclusionsViscoplasticity and PlasticityIntroductory Remarks
Viscoelasticity of Solids
Plasticity and Viscoplasticity in Small Strains
Plasticity and Viscoplasticity in Finite Strains
Damage, Cyclic Plasticity and Creep
Relationship with Microscopic Theory
Remarks on Elastoplastic Composites
Remark on the Heat EquationThermodynamics of FracturePreliminary Remark
Energy Aspects of Brittle Fracture (no thermal fields)
On Account of Thermal Fields
Material Forces in Fracture
General Features
Evaluation of Elementary Dissipation
Global Balances of Momentum
Energy Argument
The Use of Generalized Functions in the Energy Equation
Remark on Cases Exhibiting Local DissipationNon-Equilibrium Thermodynamics of Electromagnetics MatherialsGeneral Remarks
Reminder on Electromagnetism
Thermomechanics of Electromagnetic Materials
Classical Irreversible Processes: Conduction and Relaxation
Rigid Bodies
Fluids
Deformable Solids
Thermodynamics with Internal Variables
Magnetic Solids in Small Strains
Electrically Polarized Solids in Finite Strains
Dielectric Relaxation in Ceramics
Delayed-Wave Analysis
Instantaneous Wave
Electro- and Magnetomechanical Hysteresis
Electric Bodies
Magnetic Bodies
Relation to Microscopic Descriptions
Elastic Superconductors
Solutions of Polyelectrolytes
Thermodynamical Modeling
Field Equations
Dissipative Processes
Mechano-Chemical Effect
Electrically Induced Conformational Phase Transition
Kerr Effect
Ferroelectrics and Ferromagnets
Deformable Ferromagnets
Elastic Ferroelectrics
Solutions of Magnetic Fluids
Electroelastic and Magnetoelastic Fracture
Concluding RemarksWaves and Reaction-Diffusion Systems (RDS)Preliminary Remarks
Simple RDS'
Models of Nerve-Pulse Dynamics: A Good Physical
Example of Internal-Variable Theory
Nerve-Pulse Transmission
Thermodynamics of Nerve-Pulse Dynamics:
FHN Model
Hodgkin-Huxley Model
More Complex Relaxation Equations
Some Conclusive Remarks
Coherent Phase-Transition Fronts: Another Example of Thermodynamics of Material Forces
he General Problem
Quasi-Static Progress of a Coherent
Phase-Transition Front
Heat-Conducting CaseSubject Index