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Anmerkung: Intro -- Preface -- Contents -- Fundamentals of Magneto-Electro-Mechanical Couplings: Continuum Formulations and Invariant Requirements -- 1 Introduction -- 2 Foundations of Magneto-Electro Couplings -- 2.1 Preliminaries, Definitions and Units -- 2.2 A Primer in Electrostatics -- 2.3 A Primer in Magnetostatics -- 2.4 Maxwell's Equations -- 2.5 Special Cases -- 2.6 Electromagnetic Waves in Vacuum -- 2.7 Jump Conditions Across Interfaces -- 2.8 Poynting's Theorem -- 2.9 Maxwell Stress Tensor -- 3 Thermodynamics -- 3.1 First Law of Thermodynamics, Balance of Energy -- 3.2 Second Law of Thermodynamics, Entropy Inequality -- 3.3 Thermodynamic Potentials -- 4 Rotation, Spatial Reflection, Time-Reversal -- 4.1 Lorentz Invariance -- 4.2 Galilean Transformation -- 4.3 calT-Symmetry -- 4.4 Crystal Classes and Magnetic Crystal Classes -- 5 Piezoelectricity, Piezomagnetism, Some Foundations -- 5.1 Piezoelectricity -- 5.2 Piezomagnetism -- 5.3 Magnetoelectricity -- 5.4 Anisotropic and Isotropic Tensor Functions -- 6 Summary -- References -- Ferroelectric and Ferromagnetic Phase Field Modeling -- 1 Introduction -- 2 Maxwell's Equations and Polarization -- 2.1 Electro-Statics -- 3 Magnetism -- 3.1 Magneto-Statics Review -- 4 Mechano-Statics Review -- 5 Thermodynamics of Ferroelectric and Ferromagnetic Materials -- 5.1 Ferroelectric Materials: External Mechanical, Electrical Work -- and Heat Addition -- 5.2 Balance Laws for Internal Fields -- 5.3 Phase-Field Model of Ferroelectrics -- Dissipative Evolution of Domains -- Second Law of Thermodynamics -- 5.4 Internal Energy -- 5.5 Series Expansions for the Energy Functions -- 5.6 Phase-Field Modeling of Ferromagnetics -- 5.7 Finite Element Implementation -- 5.8 Example of Strain-Mediated Multiferroic Phase-Field Modeling -- References -- Semiconductor Effects in Ferroelectrics -- 1 Introduction. , 2 Thermodynamics of a Ferroelectric -- 2.1 Material Properties, Tensors, and Summation Rules -- 2.2 The Thermodynamic Energy Approach -- 2.3 The Landau-Devonshire Polynomial Approximation -- 2.4 The Depolarizing Field -- 3 Energetics of a Semiconductor -- 3.1 The Band Structure -- 3.2 Electron Statistics -- 3.3 Semiconductors with Impurities -- 3.4 Semiconductor with both Donors and Acceptors -- 3.5 Transport of Charge Carriers -- 3.6 Metal-Semiconductor Junctions -- 3.7 Heterojunctions -- 3.8 Structural Defects -- 4 The Ferroelectric Semiconductor -- 4.1 Energy Value Considerations -- 4.2 A Joint Energy Function -- 4.3 Screening -- 4.4 Maxwell-Wagner-Relaxation -- 4.5 The Electronic Impact of Defects -- 5 Case Studies -- 5.1 The Domain Wall -- 5.2 The PTCR-Effect at the Grain Boundary -- 5.3 Magnetoelectric Composites -- 5.4 Polarization Stability in Heterostructures -- 6 Conclusion and Outlook -- References -- Electromechanical Models of Ferroelectric Materials -- 1 Introduction -- 2 Origins of Ferroelectricity and Piezoelectricity -- 3 Piezoelectric Composites -- 3.1 Example of a Piezoelectric Composite -- 4 Models of Ferroelectric Switching -- 4.1 Classical Plasticity Model -- 4.2 Crystal Plasticity Model -- 4.3 Example of Crystal Plasticity Model -- 5 Models of Ferroelectric Domain Patterns -- 5.1 Theory of Compatibility -- 5.2 Average Compatibility -- 5.3 Exact Compatibility -- 5.4 Examples of Compatible Laminates -- 5.5 Evolution of Laminate Domain Patterns -- 5.6 Example of Domain Pattern Evolution -- 6 Summary and Outlook -- References -- An FE2-Scheme for Magneto-Electro-Mechanically Coupled Boundary Value Problems -- 1 Introduction -- 2 Theory of the Two-Scale Homogenization Scheme -- 2.1 Boundary Value Problems and Scale Transition -- 2.2 Discretizations of the Boundary Value Problems. , 2.3 Consistent Linearization of Macroscopic Field Equations -- 3 Magneto-Electro-Mechanical Material Models -- 3.1 Linear Piezoelectric and Piezomagnetic Model -- 3.2 Nonlinear Electrostrictive Model -- 3.3 Piezoelectric Model with Tetragonal Symmetry -- 4 Numerical Examples -- 4.1 Electrostrictive/Piezomagnetic Cantilever Beam -- 4.2 Piezoelectric/Piezomagnetic Composites -- 4.3 Ferroelectric Matrix with Cylindrical Magnetic Inclusions -- 4.4 Ferroelectric Matrix with Ellipsoidal Magnetic Inclusions -- 5 Summary -- References -- Multiscale Modeling of Electroactive Polymer Composites -- 1 Introduction -- 2 Governing Equations of Electro-Elasto-Statics at Finite Strains -- 3 Electro-Elasto-Static Boundary Value Problems on the Macro- and the Micro-scale -- 3.1 Boundary Value Problem on the Macroscopic Scale -- 3.2 Definition of Macroscopic Quantities via Homogenization -- 3.3 Boundary Value Problem on the Microscopic Scale -- 3.4 Consistent Linearization of Macroscopic Field Equations -- 4 Numerical Examples -- 4.1 Determination of the Effective Response of Electroactive Polymers with Spherical and Ellipsoidal Inclusions -- 4.2 Multiscale Simulation of Electromechanical Actuator with Composite Microstructure -- 5 Summary and Outlook -- References.