Configurational Forces ─ Thermomechanics, Physics, Mathematics, and Numerics

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.

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.

IntroductionContinuum Mechanics in the Twentieth CenturyThe Objective of This BookThe Contents of This BookHistorical Note
Standard Continuum MechanicsTheory of Motion and DeformationBasic Thermomechanics of ContinuaExamples of Thermomechanical Behaviors
Eshelbian Mechanics for Elastic BodiesThe Notion of Eshelby Material StressEshelby Stress in Small Strains in ElasticityClassical Introduction of the Eshelby Stress by Eshelby’s Original ReasoningAnother Example Due to Eshelby: Material Force on an Elastic InhomogeneityGradient Elastic MaterialsInterface in a CompositeThe Case of a Dislocation Line (Peach–Koehler Force)Four Formulations of the Balance of Linear MomentumVariational Formulations in ElasticityMore Material Balance LawsEshelby Stress and Kröner’s Theory of Incompatibility
Field TheoryIntroductionElements of Field Theory: Variational FormulationApplication to ElasticityConclusive Remarks
Canonical Thermomechanics of Complex ContinuaIntroductionReminderCanonical Balance Laws of Momentum and EnergyExamples without Body ForceVariable α as an Additional Degree of FreedomComparison with the Diffusive Internal-Variable TheoryExample: Homogeneous Dissipative Solid Material Described by Means of a Scalar Diffusive Internal VariableConclusion and Comments
Local Structural Rearrangements of Matter and Eshelby StressChanges in the Reference ConfigurationMaterial Force of InhomogeneitySome Geometric ConsiderationsContinuous Distributions of DislocationsPseudo-Inhomogeneity and Pseudo-Plastic EffectsA Variational Principle in Nonlinear Dislocation TheoryEshelby Stress as a Resolved Shear StressSecond-Gradient TheoryContinuous Distributions of Disclinations
Discontinuities and Eshelby StressesIntroductionGeneral Jump Conditions at a Moving Discontinuity SurfaceThermomechanical Shock WavesThermal Conditions at Interfaces in Thermoelastic CompositesPropagation of Phase-Transformation FrontsOn Internal and Free EnergiesThe Case of Complex MediaApplications to Problems of Materials Science (Metallurgy)
Singularities and Eshelby StressesThe Notion of Singularity SetThe Basic Problem of Fracture and Its SingularityGlobal Dissipation Analysis of Brittle FractureThe Analytical Theory of Brittle FractureSingularities and Generalized FunctionsVariational Inequality: Fracture CriterionDual I-Integral of FractureOther Material Balance Laws and Path-Independent IntegralsGeneralization to Inhomogeneous BodiesGeneralization to Dissipative BodiesA Curiosity: "Nondissipative" Heat Conductors
Generalized ContinuaIntroductionField Equations of Polar ElasticitySmall-Strain and Small-Microrotation ApproximationDiscontinuity Surfaces in Polar MaterialsFracture of Solid Polar MaterialsOther Microstructure Modelings
Systems with Mass Changes and/or DiffusionIntroductionVolumetric GrowthFirst-Order Constitutive Theory of GrowthApplication: Anisotropic Growth and Self-AdaptationIllustrations: Finite-Element ImplementationIntervention of NutrimentsEshelbian Approach to Solid–Fluid MixturesSingle-Phase Transforming Crystal and Diffusion
Electromagnetic MaterialsMaxwell Could Not Know Noether’s Theorem but…Electromagnetic Fields in Deformable Continuous MatterVariational Principle Based on the Direct MotionVariational Principle Based on the Inverse MotionGeometrical Aspects and Material UniformityRemark on Electromagnetic MomentaBalance of Canonical Momentum and Material ForcesElectroelastic Bodies and FractureTransition Fronts in Thermoelectroelastic CrystalsThe Case of Magnetized Elastic Materials
Application to Nonlinear WavesWave Momentum in Crystal MechanicsConservation Laws in Soliton TheoryExamples of Solitonic Systems and Associated QuasiparticlesSine Gordon Equation and Associated EquationsNonlinear Schrödinger Equation and Allied SystemsDriving Forces Acting on SolitonsA Basic Problem of Materials Science: Phase-Transition Front Propagation
Numerical ApplicationsIntroductionFinite-Difference Method Finite-Volume Method—Continuous Cellular AutomataFinite-Element MethodConclusive Remarks
More on Eshelby-Like Problems and SolutionsIntroductionAnalogy: Path-Independent Integrals in Heat and Electricity ConductionsThe Eshelbian Nature of Aerodynamic ForcesThe World of Configurational Forces
Bibliography
Index