Kooperativer Bibliotheksverbund

UID:

Umfang: 1 online resource (340 pages)

Ausgabe: First edition.

ISBN: 9783031519208

Serie: Springer Series in Solid and Structural Mechanics Series ; Volume 14

Anmerkung: Intro -- Preface -- Contents -- List of Figures -- 1 Introduction -- 1.1 Some General Features -- 1.2 Description of the Motion -- 1.3 Homogeneous Deformations -- 1.4 The Mobility and the Interactions -- 1.4.1 On the Initial Configuration -- 1.5 Conservation of Energy and Entropy Production -- 1.6 The Linear Thermoelasticity -- 1.7 More General Cases -- 1.7.1 Generalized Standard Materials -- 1.7.2 Linear Visco-elastic Behaviour -- 1.7.3 Normality Rule -- 1.8 The Quasistatic Evolution -- 1.8.1 Dissipative Function -- 1.8.2 The Isothermal Boundary Value Problem -- 1.9 The Lagrangian and the Dynamical Case -- 1.10 The Hamiltonian -- 1.11 Some Properties -- 1.11.1 Expression of the Conservation of Energy -- 1.11.2 Conservation Law -- 1.11.3 Property of Stationarity -- 1.12 On Discontinuities -- 1.12.1 Change of Scale -- References -- 2 Non-linear and Linear Elasticity -- 2.1 Introduction -- 2.2 Universal Deformation -- 2.3 Properties of Equilibrium Solution -- 2.4 Example of Non-linear Elastic Deformation -- 2.4.1 The Flexion of a Prismatic Bar -- 2.4.2 The Antiplane-Shear -- 2.5 Linear Elasticity: Small Perturbations -- 2.6 Equilibrium Solution of a Linear Elastic Body -- 2.7 Stability and Bifurcation in Non-linear Elasticity -- 2.7.1 Notion of Stability -- 2.7.2 The Metronome -- 2.7.3 The Euler Column -- References -- 3 Elasto-plasticity -- 3.1 Introduction -- 3.2 The Domain of Reversibility -- 3.3 The Evolution of Internal State -- 3.4 A Model of Perfect Plasticity -- 3.5 The Rate Boundary Value Problem -- 3.5.1 Characterization of Equilibrium -- 3.5.2 The Internal State Evolution -- 3.5.3 Primal Formulation -- 3.6 On the Adjoin State of Evolution Problem -- 3.7 Cyclic Plasticity -- 3.8 Classical Solutions in Elasto-plasticity -- 3.8.1 A Three Bars Lattice Under Traction -- 3.8.2 Case of a Hollow Sphere -- 3.9 Finite Elasto-plasticity. , 3.9.1 Case of Homogeneous Polycristal -- 3.10 Stability and Bifurcation in Elastoplasticity -- 3.10.1 The Shanley Column -- 3.10.2 A Model of Elastoplastic Beam -- References -- 4 Fracture Mechanics -- 4.1 Introduction -- 4.2 Case of Linear Elasticity -- 4.3 Crack Propagation in Plane Conditions -- 4.4 Energetical Interpretation -- 4.5 Invariance and J-integral -- 4.6 Dual Approach in Linear Elasticity -- 4.7 On the Rate Boundary Value Problem -- 4.8 Interaction of Cracks -- 4.9 Stability and Uniqueness: A Simple Example -- 4.10 Case of Hyperelasticity -- 4.11 Case of Dynamics -- 4.12 On Inhomogeneous Body -- 4.12.1 On the Rate Boundary Value Problem -- 4.13 Asymptotic Fields Near a Planar Crack in Linear Elasticity -- 4.13.1 Invariant Integrals upper JJ, upper G Subscript thetaGθ -- 4.13.2 Mode I -- 4.13.3 Mode II -- 4.13.4 Mode III -- 4.13.5 General Remark -- 4.14 Separation of the Modes of Rupture -- 4.15 For a Non Planar Crack -- References -- 5 Moving Discontinuities -- 5.1 Introduction -- 5.2 Dissipation Analysis -- 5.2.1 In the Dynamical Case -- 5.3 General Features for Quasi-static Evolution -- 5.4 Moving Discontinuity -- 5.4.1 The Equilibrium State -- 5.4.2 Variations of the Potential Energy -- 5.4.3 Dissipation and Evolution of the Interface -- 5.4.4 Examples on a Bar -- 5.4.5 A Model with Dissipation: A Quasi-brittle Material -- 5.5 Problem of Evolution -- 5.6 The Rate Boundary Value Problem -- 5.6.1 Stability and Bifurcation -- 5.7 An Example -- 5.8 Connection with Fracture -- 5.8.1 The Quasi-Crack Problem -- 5.8.2 Peculiar Solutions of Equilibrium Equation -- 5.9 The Quasi-Crack Solution in Mode III -- 5.9.1 Determination of the Constants -- 5.9.2 Solutions for alpha greater than or equals 0αge0 -- 5.9.3 Solution for alpha less than or equals 0αle0 -- 5.9.4 A Particular Constitutive Law -- 5.9.5 The Particular Case alpha equals 0α=0. , References -- 6 Damage Modelling and Initiation of Defect -- 6.1 Introduction -- 6.2 A Simple Local Damage Model -- 6.2.1 Evolution of Damage Parameter -- 6.2.2 Properties of Damage Field -- 6.2.3 Models with Local Discontinuities: An Axial Description -- 6.3 Models with Damage Gradient -- 6.3.1 The Total Potential Energy and its Variations -- 6.3.2 On the Bar in Extension -- 6.4 A Model of Graded Damage -- 6.4.1 The Equilibrium Problem -- 6.4.2 On the Regularity of the Fields -- 6.4.3 The Total Potential Energy -- 6.4.4 The Bar Under Uni-axial Extension -- 6.5 A Regularized Graded Damage Model -- 6.5.1 On the Bar in Extension -- 6.6 Comparison Between Graded Damage and Thick-Level Set Model -- 6.6.1 Model with Convex Constrains -- 6.7 The State of Equilibrium -- 6.7.1 On the Evolution of Damage -- 6.8 On the Rate Boundary Value Problem -- 6.9 On the Role of the Curvature: Example on a Sphere -- 6.9.1 The Inhomogeneous Sphere Under Radial Loading -- 6.9.2 The Sharp Interface -- 6.9.3 A Graded Damaged Sphere -- 6.10 Coupling with Plasticity -- 6.10.1 Sharp Interface -- 6.10.2 Solution with Transfer of Internal State -- 6.10.3 Sharp Versus Diffuse Interface -- References -- 7 A Thermodynamical Approach to Contact Wear -- 7.1 Introduction -- 7.2 The Energetical Approach -- 7.3 The Dissipation -- 7.3.1 Interface Propagation Law -- 7.3.2 Description of the Interface -- 7.4 An Application of the Model -- 7.5 Global Approach of the Interface -- 7.6 On Change of the Contact Surface -- References -- 8 Delamination of Laminates -- 8.1 Introduction -- 8.2 The Kinematic of the Plates -- 8.3 Conservation of the Momentum -- 8.4 Dissipation Analysis -- 8.5 The Rate Boundary Value Problem -- 8.6 Delamination of a Thin Membrane Under Pressure -- References -- 9 On Relationships Between Micro-Macro Quantities -- 9.1 Introduction. , 9.2 Mode and Process of Localization -- 9.3 Potentials and General Properties -- 9.4 Macrohomogeneous Body and Linear Elasticity -- 9.5 On the Decomposition of the Macroscopic Strain -- 9.6 Moving Interfaces -- 9.7 Case of Linear Elastic Phases -- 9.8 More General Cases -- 9.9 The Composite Sphere Assemblage -- 9.10 Extension to Finite Deformation -- 9.11 From Monocrystal to Polycrystal -- 9.11.1 On the Elastic Behaviour -- 9.11.2 On Elastoplastic Behaviour -- References -- 10 Homogenization in Linear Elasticity -- 10.1 The Problem of Inhomogeneous Elasticity -- 10.2 Introduction of a Comparison Material -- 10.3 Isotropic Spatial Distribution of Mechanical Phases -- 10.4 On Particulate Composite Material -- 10.5 On the Hashin's Spheres Assemblage -- 10.6 Extension to Imperfect Interface -- 10.6.1 Estimation of the Global Behaviour -- 10.6.2 Choice of the Reference Medium -- 10.6.3 Interpretation -- 10.6.4 Case of Conduction -- 10.6.5 Evaluation of upper Q left parenthesis upper K Subscript o Baseline right parenthesisQ(Ko) and upper Q asterisk left parenthesis 1 divided by upper K Subscript o Baseline right parenthesisQ*(1/Ko) -- References -- 11 Optimal Control and Non Linear Inverse Problems -- 11.1 Inverse Problems in Linear Elasticity -- 11.1.1 The Problem Setting -- 11.1.2 A Well Posed Problem -- 11.1.3 The Idea of Control -- 11.1.4 The Optimization Method -- 11.2 Inverse Problem in Elastoplasticity -- 11.2.1 Inverse Problems on Three Bars Lattice -- 11.2.2 Inverse Problem When h Subscript o Baseline equals 0ho=0 -- 11.3 Estimation of the Internal State in Elastoplasticity -- 11.3.1 The Inverse Problem on a Sphere -- 11.4 Boundary Control and Extension in Viscoplasticity -- References -- 12 Conclusion -- Appendix A Tensorial Analysis -- A.1 Bilinear form Associated to a Linear Mapping -- A.2 Euclidean Vector Space -- A.3 Differential Operators. , A.3.0.1 Cartesian Coordinates -- A.3.0.2 On Other Basis -- Appendix B General Relations -- B.1 Continuous Case -- B.2 Discontinuous Case -- Appendix C Particular Solution in Linear Elasticity -- C.1 Cylinders and Spheres Under Radial Loading -- C.1.1 Case of Uniform lamdaλ -- C.2 A Cylindrical or Spherical Shell Under Shear -- C.3 Fundamental Linear Elastic Solution -- C.3.1 Plane Isotropic Elasticity -- C.3.2 3D-Elasticity -- C.3.3 Case of on Half Plane in Plane Strain -- C.4 Anti-plane Elasticity -- C.4.1 Case of the Half-plane y greater than 0y> -- 0 -- Appendix D Hodograph Transformation -- Appendix E Convex Analysis -- Appendix F Optimal Control -- Appendix G Some Integrals -- Index.

Weitere Ausg.: ISBN 9783031519192

Sprache: Englisch