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Intro; Preface; Contents; Contributors; 1 Damping in Materials and Structures: An Overview; Abstract; 1.1 Introduction; 1.2 Mechanisms of Energy Dissipation; 1.2.1 Macroscopic Approach; 1.2.1.1 Viscous Dissipation; 1.2.1.2 Friction Dissipation; 1.2.1.3 Magneto-Mechanic Dissipation; 1.2.1.4 Electro-Mechanic Dissipation; 1.2.1.5 Plastic Dissipation; 1.2.2 Microscopic Approach; 1.2.2.1 Atomic Scale Approach; 1.2.2.2 Molecular Scale Approach; 1.2.2.3 Mesoscopic Scale Approach; 1.3 Modelling Energy Dissipation; 1.3.1 Internal Forces; 1.3.2 Work of Internal Forces: Cycling
1.3.3 Viscous Dissipation1.3.3.1 Linear Behavior of the Phenomenon; Discrete Bi-parametric Model (Like Voigt Model); Continuous Multi-parametric Model (Prony Series); 1.3.3.2 Non-linear Behavior of the Phenomenon; Schapery Model; Valanis-Landel Model; Frechet-Volterra Series Model; Linearization of the Phenomenon; 1.3.4 Friction Dissipation; 1.3.4.1 Coulomb's Friction Modelling; 1.3.4.2 Tresca's Friction Modelling; 1.3.4.3 Dahl's Friction Modelling; 1.3.4.4 Micro-friction; 1.4 Conclusion; References
2 The Principle of Virtual Power (PVP): Application to Complex Media, Extension to Gauge and Scale Invariances, and Fundamental AspectsAbstract; 2.1 First Part; 2.1.1 Complex Media: Modeling of the Different Continua; 2.1.2 Thermo-Electro-Magneto-Mechanical Equations; 2.1.2.1 General Principles in Global Form; 2.1.2.2 Local Electro-Magneto-Mechanical Balance Equations; 2.1.2.3 Local Thermodynamical Equations; 2.1.3 Clausius-Duhem Inequality; 2.2 Second Part; 2.2.1 Extension of the PVP to Gauge and Scale Invariances; 2.2.2 Extended form of d'Alembert's Principle; 2.2.3 Unified Global Statement
2.2.4 Derivation of Scale, Gauge and Rotational Invariances2.2.5 Local Equations; 2.2.6 Relativistic Framework; 2.3 Third Part; 2.3.1 Foundation of the Principle of Virtual Power (PVP); 2.3.2 Main Points of the Leibnizian Dynamical Framework; 2.3.3 Determination of the Yet Under-Determinate Framework; 2.3.4 Deduction of the PVP Based on Duality; 2.3.5 Derivation of Einstein's Dynamics; Acknowledgements; References; 3 The Limitations and Successes of Concurrent Dynamic Multiscale Modeling Methods at the Mesoscale; Abstract; 3.1 Introduction; 3.2 Review of Dynamic Multiscale Methods
3.2.1 Coupled Atomistic and Discrete Dislocation Dynamics3.2.2 Coupled Extended Finite Element Method; 3.2.3 Concurrent Atomistic Continuum Method; 3.2.4 The Hot Quasi-Continuum Method; 3.2.5 The Atomistic to Continuum Method; 3.3 Analysis; 3.3.1 Modeling Materials Beyond Monoatomic Crystals; 3.3.2 Modeling of Defects and Waves; 3.4 Conclusions; Acknowledgements; References; 4 Modeling Semiconductor Crystal Growth Under Electromagnetic Fields; Abstract; 4.1 Introduction; 4.1.1 Liquid Phase Electroepitaxy; 4.1.2 Traveling Heater Method
1.3.3 Viscous Dissipation1.3.3.1 Linear Behavior of the Phenomenon; Discrete Bi-parametric Model (Like Voigt Model); Continuous Multi-parametric Model (Prony Series); 1.3.3.2 Non-linear Behavior of the Phenomenon; Schapery Model; Valanis-Landel Model; Frechet-Volterra Series Model; Linearization of the Phenomenon; 1.3.4 Friction Dissipation; 1.3.4.1 Coulomb's Friction Modelling; 1.3.4.2 Tresca's Friction Modelling; 1.3.4.3 Dahl's Friction Modelling; 1.3.4.4 Micro-friction; 1.4 Conclusion; References
2 The Principle of Virtual Power (PVP): Application to Complex Media, Extension to Gauge and Scale Invariances, and Fundamental AspectsAbstract; 2.1 First Part; 2.1.1 Complex Media: Modeling of the Different Continua; 2.1.2 Thermo-Electro-Magneto-Mechanical Equations; 2.1.2.1 General Principles in Global Form; 2.1.2.2 Local Electro-Magneto-Mechanical Balance Equations; 2.1.2.3 Local Thermodynamical Equations; 2.1.3 Clausius-Duhem Inequality; 2.2 Second Part; 2.2.1 Extension of the PVP to Gauge and Scale Invariances; 2.2.2 Extended form of d'Alembert's Principle; 2.2.3 Unified Global Statement
2.2.4 Derivation of Scale, Gauge and Rotational Invariances2.2.5 Local Equations; 2.2.6 Relativistic Framework; 2.3 Third Part; 2.3.1 Foundation of the Principle of Virtual Power (PVP); 2.3.2 Main Points of the Leibnizian Dynamical Framework; 2.3.3 Determination of the Yet Under-Determinate Framework; 2.3.4 Deduction of the PVP Based on Duality; 2.3.5 Derivation of Einstein's Dynamics; Acknowledgements; References; 3 The Limitations and Successes of Concurrent Dynamic Multiscale Modeling Methods at the Mesoscale; Abstract; 3.1 Introduction; 3.2 Review of Dynamic Multiscale Methods
3.2.1 Coupled Atomistic and Discrete Dislocation Dynamics3.2.2 Coupled Extended Finite Element Method; 3.2.3 Concurrent Atomistic Continuum Method; 3.2.4 The Hot Quasi-Continuum Method; 3.2.5 The Atomistic to Continuum Method; 3.3 Analysis; 3.3.1 Modeling Materials Beyond Monoatomic Crystals; 3.3.2 Modeling of Defects and Waves; 3.4 Conclusions; Acknowledgements; References; 4 Modeling Semiconductor Crystal Growth Under Electromagnetic Fields; Abstract; 4.1 Introduction; 4.1.1 Liquid Phase Electroepitaxy; 4.1.2 Traveling Heater Method