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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

UID:

Umfang: 1 Online-Ressource (XV, 334 Seiten)

ISBN: 9783031519208

Serie: Springer series in solid and structural mechanics volume 14

Inhalt: This book presents an introduction to the non-linear mechanics of materials, focusing on a unified energetical approach. It begins by summarizing the framework of a thermodynamic description of continua, including a description of the kinematics of deformation, and a summary of the equations of motion. After a short description of the motion of the system and the mechanical interaction, the book introduces the Lagrangean and Hamiltonian functionals of the system, transitioning to the quasistatic characterization with emphasis on the role of potential energy and pseudo-potential of dissipation. The framework is then extended to fracture and damage mechanics with a similar energetical approach proposed for material damage and wear. The book looks at homogenization in non-linear mechanics for locally plastic or damaged material with an analysis of stability and bifurcation of the equilibrium path. Lastly, inverse problems in non-linear mechanics are introduced using optimal control theory. All the concepts introduced in the book are illustrated using analytical solutions on beams, rods, plates, or using spherical and cylindrical symmetries. Graduate students and researchers working on continuum mechanics and interested in a deeper understanding of materials damage, wear, and fatigue will find this book instructive and informative.

Anmerkung: Chapter 1. Introduction -- Chapter 2. Non-linear and linear elasticity -- Chapter 3. Elasto-plasticity -- Chapter 4. Fracture Mechanics -- Chapter 5. Moving Discontinuities -- Chapter 6. Damage modelling and initiation of defect -- Chapter 7. A thermodynamical approach to contact wear -- Chapter 8. Delamination of laminates -- Chapter 9. Micro-macro relations -- Chapter 10. Homogenization in linear elasticity -- Chapter 11. Optimal control and non linear inverse problems -- Chapter 12. Conclusion.

Weitere Ausg.: ISBN 9783031519192

Weitere Ausg.: ISBN 9783031519215

Weitere Ausg.: ISBN 9783031519222

Weitere Ausg.: Erscheint auch als Druck-Ausgabe Stolz, Claude Introduction to non-linear mechanics Cham : Springer, 2024 ISBN 9783031519192

Sprache: Englisch

Schlagwort(e): Werkstoffmechanik ; Nichtlineare Mechanik

DOI: 10.1007/978-3-031-51920-8

URL: lizenzpflichtig