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Foreword; Preface; Fluid-structure Interactions; Scope of this Book; Acknowledgments; Contents; Part I Fundamentals; 1 Introduction; 1.1 Applications for Fluid-structure Interactions; 1.2 Dynamics of Fluid-structure Interactions; 1.3 Mathematical Challenges; 1.4 Partitioned Approaches; 1.5 Monolithic Models and Finite Element Discretizations; 1.6 Outline; 2 Models; 2.1 Continuum Mechanics; 2.1.1 Coordinate Systems; 2.1.2 Deformation Gradient; 2.1.3 Strain; 2.1.4 Rate of Deformation and Strain Rate; 2.1.5 Stress; 2.1.6 Conservation Principles
2.1.7 Conservation Principles in Different CoordinateSystems2.2 Material Laws; 2.2.1 Hyperelastic Materials; 2.2.2 Linearizations; 2.2.3 Incompressible Materials; 2.3 The Solid Problem; 2.3.1 The Navier-Lamé Equations; 2.3.1.1 The Incompressible Navier-Lamé Equations ; 2.3.1.2 The Non-stationary Navier-Lamé Equations; 2.3.2 Theory of Nonlinear Hyper-Elastic Material; 2.4 The Fluid Problem; 2.4.1 Boundary and Initial Conditions; 2.4.2 The ``do-nothing'' Outflow Condition; 2.4.3 Reynolds Number; 2.4.4 The Linear Stokes Equations; 2.4.5 Theory of Incompressible Flows
2.4.5.1 Existence and Uniqueness of Solutions to the Stokes Equations2.4.5.2 Existence and Uniqueness of the Pressure; 2.4.5.3 The Stationary Navier-Stokes Equations; 2.4.5.4 The Non-stationary Navier-StokesEquations; 2.5 Flow Problems on Moving Domains; 2.5.1 Eulerian Techniques for Flow Problems on Moving Domains; 2.5.2 The Arbitrary Lagrangian Eulerian (ALE) Formulation for Moving Domain Problems; 2.5.3 Definition of the ALE Map; 3 Coupled Fluid-structure Interactions; 3.1 Coupling Conditions; 3.1.1 The Kinematic Condition; 3.1.2 The Dynamic Condition; 3.1.3 The Geometric Condition
3.1.4 Interface Regularity and Boundary Conditions3.1.5 Coupled Fluid-structure Interaction; 3.2 Existence and Uniqueness Theory for Fluid-structureInteractions; 3.3 The Added Mass Effect; 3.4 Variational Coupling Techniques; 3.5 Fluid-structure Interactions in ALE Coordinates; 3.5.1 Definition of the ALE Map; 3.5.2 Coupled ALE Formulation ; 3.6 Fully Eulerian Formulation for the Fluid-structure Interaction Problem; 3.6.1 Elastic Structures in Eulerian Coordinates; 3.6.2 Fluid-structure Interaction in Eulerian Coordinates; 3.6.3 The Initial Point Set Method; 4 Discretization
2.1.7 Conservation Principles in Different CoordinateSystems2.2 Material Laws; 2.2.1 Hyperelastic Materials; 2.2.2 Linearizations; 2.2.3 Incompressible Materials; 2.3 The Solid Problem; 2.3.1 The Navier-Lamé Equations; 2.3.1.1 The Incompressible Navier-Lamé Equations ; 2.3.1.2 The Non-stationary Navier-Lamé Equations; 2.3.2 Theory of Nonlinear Hyper-Elastic Material; 2.4 The Fluid Problem; 2.4.1 Boundary and Initial Conditions; 2.4.2 The ``do-nothing'' Outflow Condition; 2.4.3 Reynolds Number; 2.4.4 The Linear Stokes Equations; 2.4.5 Theory of Incompressible Flows
2.4.5.1 Existence and Uniqueness of Solutions to the Stokes Equations2.4.5.2 Existence and Uniqueness of the Pressure; 2.4.5.3 The Stationary Navier-Stokes Equations; 2.4.5.4 The Non-stationary Navier-StokesEquations; 2.5 Flow Problems on Moving Domains; 2.5.1 Eulerian Techniques for Flow Problems on Moving Domains; 2.5.2 The Arbitrary Lagrangian Eulerian (ALE) Formulation for Moving Domain Problems; 2.5.3 Definition of the ALE Map; 3 Coupled Fluid-structure Interactions; 3.1 Coupling Conditions; 3.1.1 The Kinematic Condition; 3.1.2 The Dynamic Condition; 3.1.3 The Geometric Condition
3.1.4 Interface Regularity and Boundary Conditions3.1.5 Coupled Fluid-structure Interaction; 3.2 Existence and Uniqueness Theory for Fluid-structureInteractions; 3.3 The Added Mass Effect; 3.4 Variational Coupling Techniques; 3.5 Fluid-structure Interactions in ALE Coordinates; 3.5.1 Definition of the ALE Map; 3.5.2 Coupled ALE Formulation ; 3.6 Fully Eulerian Formulation for the Fluid-structure Interaction Problem; 3.6.1 Elastic Structures in Eulerian Coordinates; 3.6.2 Fluid-structure Interaction in Eulerian Coordinates; 3.6.3 The Initial Point Set Method; 4 Discretization