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Gurtin M.E., Fried E., Anand L. The Mechanics and Thermodynamics of Continua PDF

Gurtin M.E., Fried E., Anand L. The Mechanics and Thermodynamics of Continua
Cambridge University Press, 2010, 694 pages, ISBN: 052140598X

The Mechanics and Thermodynamics of Continua presents a unified treatment of continuum mechanics and thermodynamics that emphasizes the universal status of the basic balances and the entropy imbalance. These laws are viewed as fundamental building blocks on which to frame theories of material behavior. As a valuable reference source, this book presents a detailed and complete treatment of continuum mechanics and thermodynamics for graduates and advanced undergraduates in engineering, physics, and mathematics. The chapters on plasticity discuss the standard isotropic theories and, in addition, crystal plasticity and gradient plasticity.

Vector and tensor algebra
Vector Algebra
Tensor Algebra

Vector and tensor analysis
Differentiation
Integral Theorems

Kinematics
Motion of a Body
The Deformation Gradient
Stretch, Strain, and Rotation
Deformation of Volume and Area
Material and Spatial Descriptions of Fields
Special Motions
Stretching and Spin in an Arbitrary Motion
Material and Spatial Tensor Fields. Pullback and Pushforward Operations
Modes of Evolution for Vector and Tensor Fields
Motions with Constant Velocity Gradient
Material and Spatial Integration
Reynolds’ Transport Relation. IsochoricMotions

Basic mechanical principles
Balance of Mass
Forces and Moments. Balance Laws for Linear and Angular Momentum
Frames of Reference
Frame-Indifference Principle
Alternative Formulations of the Force and Moment Balances
Mechanical Laws for a Spatial Control Volume
Referential Forms for the Mechanical Laws
Further Discussion of Stress

Basic thermodynamical principles
The First Law: Balance of Energy
The Second Law: Nonnegative Production of Entropy
General Theorems
A Free-Energy Imbalance for Mechanical Theories
The First Two Laws for a Spatial Control Volume
The First Two Laws Expressed Referentially

Mechanical and thermodynamical laws at a shock wave
Shock Wave Kinematics
Basic Laws at a Shock Wave: Jump Conditions

Interlude: basic hypotheses for developing physically meaningful constitutive theories
General Considerations
Constitutive Response Functions
Frame-Indifference and Compatibility with Thermodynamics

Rigid heat conductors
Basic Laws
General Constitutive Equations
Thermodynamics and Constitutive Restrictions: The Coleman–Noll Procedure
Consequences of the State Restrictions
Consequences of the Heat-Conduction Inequality
Fourier’s Law

The mechanical theory of compressible and incompressible fluids
Brief Review
Elastic Fluids
Compressible, Viscous Fluids
Incompressible Fluids

Mechanical theory of elastic solids
Brief Review
Constitutive Theory
Summary of Basic Equations. Initial/Boundary-Value Problems
Material Symmetry
Simple Shear of a Homogeneous, Isotropic Elastic Body
The Linear Theory of Elasticity
Digression: Incompressibility
Incompressible Elastic Materials
Approximately Incompressible Elastic Materials

Thermoelasticity
Brief Review
Constitutive Theory
Natural Reference Configuration for a Given Temperature
Linear Thermoelasticity

Species diffusion coupled to elasticity
Balance Laws for Forces,Moments, and the Conventional External Power
Mass Balance for a Single Diffusing Species
Free-Energy Imbalance Revisited. Chemical Potential
Multiple Species
Digression: The Thermodynamic Laws in the Presence of Species Transport
Referential Laws
Constitutive Theory for a Single Species
Material Symmetry
Natural Reference Configuration
Summary of Basic Equations for a Single Species
Constitutive Theory for Multiple Species
Summary of Basic Equations for N Independent Species
Substitutional Alloys
Linearization

Theory of isotropic plastic solids undergoing small deformations
Some Phenomenological Aspects of the Elastic-Plastic Stress-Strain Response of PolycrystallineMetals
Formulation of the Conventional Theory. Preliminaries
Formulation of the Mises Theory of Plastic Flow
Inversion of the Mises Flow Rule: ˙E p in Terms of E˙ and T
Rate-Dependent Plastic Materials
Maximum Dissipation
Hardening Characterized by a Defect Energy
The Thermodynamics of Mises–Hill Plasticity
Formulation of Initial/Boundary-Value Problems for the Mises Flow Equations as Variational Inequalities

Small deformation, isotropic plasticity based on the principle of virtual power
Introduction
Conventional Theory Based on the Principle of Virtual Power Basic Constitutive Theory
Material Stability and Its Relation to Maximum Dissipation

Strain gradient plasticity based on the principle of virtual power
Introduction
Kinematics
The Gradient Theory of Aifantis
The Gradient Theory of Gurtin and Anand

Large-deformation theory of isotropic plastic solids
Kinematics
Virtual-Power Formulation of the Standard and Microscopic Force Balances
Free-Energy Imbalance
Two New Stresses
Constitutive Theory
Summary of the Basic Equations. Remarks
Plastic Irrotationality: The Condition Wp ≡ 0
Yield Surface. Yield Function. Consistency Condition
|Dp| in Terms of E˙ andMe
Evolution Equation for the Second Piola Stress
Rate-Dependent Plastic Materials

Theory of single crystals undergoing small deformations
Basic Single-Crystal Kinematics
The Burgers Vector and the Flow of Screw and Edge Dislocations
Conventional Theory of Single-Crystals
Single-Crystal Plasticity at Small Length-Scales: A Small-Deformation Gradient Theory

Single crystals undergoing large deformations
Basic Single-Crystal Kinematics
The Burgers Vector and the Flow of Screw and Edge Dislocations
Virtual-Power Formulation of the Standard and Microscopic Force Balances
Free-Energy Imbalance
Conventional Theory
Taylor’s Model of Polycrystal
Single-Crystal Plasticity at Small Length Scales: A Large-Deformation Gradient Theory
Isotropic Functions
The Exponential of a Tensor
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