Configurational Forces

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Opis: Configurational Forces - Gerard A. Maugin, G Maugin

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.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 Kroner'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 I 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 Schrodinger 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


Szczegóły: Configurational Forces - Gerard A. Maugin, G Maugin

Tytuł: Configurational Forces
Autor: Gerard A. Maugin, G Maugin
Producent: CRC Press Inc.
ISBN: 9781439846124
Rok produkcji: 2010
Ilość stron: 562
Oprawa: Twarda
Waga: 0.9 kg


Recenzje: Configurational Forces - Gerard A. Maugin, G Maugin

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Configurational Forces

,

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.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 Kroner'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 I 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 Schrodinger 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

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Cena 471,45 PLN
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Szczegóły: Configurational Forces - Gerard A. Maugin, G Maugin

Tytuł: Configurational Forces
Autor: Gerard A. Maugin, G Maugin
Producent: CRC Press Inc.
ISBN: 9781439846124
Rok produkcji: 2010
Ilość stron: 562
Oprawa: Twarda
Waga: 0.9 kg


Recenzje: Configurational Forces - Gerard A. Maugin, G Maugin

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