Configurational Forces: Thermomechanics, Physics, Mathematics, and Numerics, 1st Edition (Hardback) book cover

Configurational Forces

Thermomechanics, Physics, Mathematics, and Numerics, 1st Edition

By Gerard A. Maugin

Chapman and Hall/CRC

562 pages | 19 Color Illus. | 58 B/W Illus.

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Hardback: 9781439846124
pub: 2010-12-01
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pub: 2016-04-19
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Exploring recent developments in continuum mechanics, Configurational Forces: Thermomechanics, Physics, Mathematics, and Numerics presents the general framework for configurational forces. It also covers a range of applications in engineering and condensed matter physics.

The author presents the fundamentals of accepted standard continuum mechanics, before introducing Eshelby material stress, field theory, variational formulations, Noether’s theorem, and the resulting conservation laws. In the chapter on complex continua, he compares the classical perspective of B.D. Coleman and W. Noll with the viewpoint linked to abstract field theory. He then describes the important notion of local structural rearrangement and its relationship to Eshelby stress. After looking at the relevance of Eshelby stress in the thermodynamic description of singular interfaces, the text focuses on fracture problems, microstructured media, systems with mass exchanges, and electromagnetic deformable media. The concluding chapters discuss the exploitation of the canonical conservation law of momentum in nonlinear wave propagation, the application of canonical-momentum conservation law and material force in numerical schemes, and similarities of fluid mechanics and aerodynamics.

Written by a long-time researcher in mechanical engineering, this book provides a detailed treatment of the theory of configurational forces—one of the latest and most fruitful advances in macroscopic field theories. Through many applications, it shows the depth and efficiency of this theory.


"… an excellent introduction into this wide branch of mechanics, and, at the same time, it provides scientists already involved in the field extended references to specific aspects of Eshelbian mechanics. On an equal level, the thermomechanics, physics, mathematics and numerics of configurational forces are covered. Starting with elastic bodies, the theory is extended step-by-step to complex and generalized continua. Discontinuities of various kinds, fracture, moving interfaces, wave motion, etc., are treated, and elastic, elastoplastic, elastomagnetic and thermoelastic materials are discussed. The huge amount of material is arranged in a clear and rigorous manner. This is a book of a master in his field."

— Reinhold Kienzler (Bremen), Zentralblatt MATH

The book is indeed written by a true master of his field and is thus great fun to read and to study. It is of interest not only for specialists in configurational forces but for all those who are concerned with the broad field of continuum modeling. It is for example amazing to see how apparently dissimilar fields such as e1ectro-magneto-mechanics and biological growth or nonlinear waves are connected by the underlying and thus unifying concept of configurational forces. The book is extremely rich in detail and depth; at the same time it will be helpful for the beginner and the expert alike. In summary I assess that this is one of the few books that should be on the bookshelf of any researcher in mechanics and/or applied mathematics.


Table of Contents


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


Elements of Field Theory: Variational Formulation

Application to Elasticity

Conclusive Remarks

Canonical Thermomechanics of Complex Continua



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


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


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


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


Finite-Difference Method

Finite-Volume Method—Continuous Cellular Automata

Finite-Element Method

Conclusive Remarks

More on Eshelby-Like Problems and Solutions


Analogy: Path-Independent Integrals in Heat and Electricity Conductions

The Eshelbian Nature of Aerodynamic Forces

The World of Configurational Forces



About the Author

Gérard A. Maugin is a distinguished professor and research director of the Institut Jean Le Rond d’Alembert at the Université Pierre et Marie Curie and CNRS. He has taught at numerous universities around the world and has been involved in research projects with organizations such as the French Ministry of National Defense, US National Science Foundation, US Army Research Office, US Office of Naval Research, National Research Council of Canada, NATO, the European Community, and I.A.E.A-UNESCO. A member of many scientific societies, Dr. Maugin has received several awards throughout his career, including the Max Planck Research Award for Engineering Sciences given by the Max Planck Society and the Alexander von Humboldt Foundation.

About the Series

Modern Mechanics and Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Mechanics / General
SCIENCE / Physics