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Configurational Forces

Thermomechanics, Physics, Mathematics, and Numerics

Configurational Forces by Gerard A. Maugin
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Introduction
Continuum Mechanics in the Twentieth Century
The Objective of This Book
The Contents of This Book
Historical Note

Standard Continuum Mechanics
Theory of Motion and Deformation
Basic Thermomechanics of Continua
Examples of Thermomechanical Behaviors

Eshelbian Mechanics for Elastic Bodies
The Notion of Eshelby Material Stress
Eshelby Stress in Small Strains in Elasticity
Classical Introduction of the Eshelby Stress by Eshelby’s Original Reasoning
Another Example Due to Eshelby: Material Force on an Elastic Inhomogeneity
Gradient Elastic Materials
Interface in a Composite
The Case of a Dislocation Line (Peach–Koehler Force)
Four Formulations of the Balance of Linear Momentum
Variational Formulations in Elasticity
More Material Balance Laws
Eshelby Stress and Kröner’s Theory of Incompatibility

Field Theory
Introduction
Elements of Field Theory: Variational Formulation
Application to Elasticity
Conclusive Remarks

Canonical Thermomechanics of Complex Continua
Introduction
Reminder
Canonical Balance Laws of Momentum and Energy
Examples without Body Force
Variable α as an Additional Degree of Freedom
Comparison with the Diffusive Internal-Variable Theory
Example: Homogeneous Dissipative Solid Material Described by Means of a Scalar Diffusive Internal Variable
Conclusion and Comments

Local Structural Rearrangements of Matter and Eshelby Stress
Changes in the Reference Configuration
Material Force of Inhomogeneity
Some Geometric Considerations
Continuous Distributions of Dislocations
Pseudo-Inhomogeneity and Pseudo-Plastic Effects
A Variational Principle in Nonlinear Dislocation Theory
Eshelby Stress as a Resolved Shear Stress
Second-Gradient Theory
Continuous Distributions of Disclinations

Discontinuities and Eshelby Stresses
Introduction
General Jump Conditions at a Moving Discontinuity Surface
Thermomechanical Shock Waves
Thermal Conditions at Interfaces in Thermoelastic Composites
Propagation of Phase-Transformation Fronts
On Internal and Free Energies
The Case of Complex Media
Applications to Problems of Materials Science (Metallurgy)

Singularities and Eshelby Stresses
The Notion of Singularity Set
The Basic Problem of Fracture and Its Singularity
Global Dissipation Analysis of Brittle Fracture
The Analytical Theory of Brittle Fracture
Singularities and Generalized Functions
Variational Inequality: Fracture Criterion
Dual I-Integral of Fracture
Other Material Balance Laws and Path-Independent Integrals
Generalization to Inhomogeneous Bodies
Generalization to Dissipative Bodies
A Curiosity: "Nondissipative" Heat Conductors

Generalized Continua
Introduction
Field Equations of Polar Elasticity
Small-Strain and Small-Microrotation Approximation
Discontinuity Surfaces in Polar Materials
Fracture of Solid Polar Materials
Other Microstructure Modelings

Systems with Mass Changes and/or Diffusion
Introduction
Volumetric Growth
First-Order Constitutive Theory of Growth
Application: Anisotropic Growth and Self-Adaptation
Illustrations: Finite-Element Implementation
Intervention of Nutriments
Eshelbian Approach to Solid–Fluid Mixtures
Single-Phase Transforming Crystal and Diffusion

Electromagnetic Materials
Maxwell Could Not Know Noether’s Theorem but…
Electromagnetic Fields in Deformable Continuous Matter
Variational Principle Based on the Direct Motion
Variational Principle Based on the Inverse Motion
Geometrical Aspects and Material Uniformity
Remark on Electromagnetic Momenta
Balance of Canonical Momentum and Material Forces
Electroelastic Bodies and Fracture
Transition Fronts in Thermoelectroelastic Crystals
The Case of Magnetized Elastic Materials

Application to Nonlinear Waves
Wave Momentum in Crystal Mechanics
Conservation Laws in Soliton Theory
Examples of Solitonic Systems and Associated Quasiparticles
Sine Gordon Equation and Associated Equations
Nonlinear Schrödinger Equation and Allied Systems
Driving Forces Acting on Solitons
A Basic Problem of Materials Science: Phase-Transition Front Propagation

Numerical Applications
Introduction
Finite-Difference Method
Finite-Volume Method—Continuous Cellular Automata
Finite-Element Method
Conclusive Remarks

More on Eshelby-Like Problems and Solutions
Introduction
Analogy: Path-Independent Integrals in Heat and Electricity Conductions
The Eshelbian Nature of Aerodynamic Forces
The World of Configurational Forces

Bibliography

Index

CRC Press; December 2010
542 pages; ISBN 9781439846131
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Title: Configurational Forces
Author: Gerard A. Maugin
 
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