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Handbook of Peridynamic Modeling.
This handbook covers the peridynamic modeling of failure and damage. Peridynamics is a reformulation of continuum mechanics based on the integration of interactions rather than the spatial differentiation of displacements. The book extends the classical theory of continuum mechanics to allow unguide...
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Diğer Yazarlar: | , , |
Materyal Türü: | e-Kitap |
Dil: | İngilizce |
Baskı/Yayın Bilgisi: |
Milton :
CRC Press LLC,
2016.
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Edisyon: | 1st ed. |
Seri Bilgileri: | Advances in Applied Mathematics Series
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Konular: | |
Online Erişim: | Full-text access OPAC'ta görüntüle |
İçindekiler:
- Cover
- Half Title
- Title Page
- Copyright Page
- Contents
- Foreword
- Preface
- List of Figures
- List of Tables
- Contributors
- I: The Need for Nonlocal Modeling and Introduction to Peridynamics
- 1 Why Peridynamics?
- 1.1 The mixed blessing of locality
- 1.2 Origins of nonlocality in a model
- 1.2.1 Long-range forces
- 1.2.2 Coarsening a fine-scale material system
- 1.2.3 Smoothing of a heterogeneous material system
- 1.3 Nonlocality at the macroscale
- 1.4 The mixed blessing of nonlocality
- References
- 2 Introduction to Peridynamics
- 2.1 Equilibrium in terms of integral equations
- 2.2 Material modeling
- 2.2.1 Bond-based materials
- 2.2.2 Relation between bond densities and flux
- 2.2.3 Peridynamic states
- 2.2.4 Ordinary state-based materials
- 2.2.5 Correspondence materials
- 2.2.6 Discrete particles as peridynamic bodies
- 2.2.7 Setting the horizon
- 2.2.8 Linearized peridynamics
- 2.3 Plasticity
- 2.3.1 Bond-based microplastic material
- 2.3.2 LPS material with plasticity
- 2.4 Damage and fracture
- 2.4.1 Damage in bond-based models
- 2.4.2 Damage in ordinary state-based material models
- 2.4.3 Damage in correspondence material models
- 2.4.4 Nucleation strain
- 2.5 Treatment of boundaries and interfaces
- 2.5.1 Bond-based materials
- 2.5.2 State-based materials
- 2.6 Emu numerical method
- 2.7 Conclusions
- References
- II: Mathematics, Numerics, and Software Tools of Peridynamics
- 3 Nonlocal Calculus of Variations and Well-Posedness of Peridynamics
- 3.1 Introduction
- 3.2 A brief review of well-posedness results
- 3.3 Nonlocal balance laws and nonlocal vector calculus
- 3.4 Nonlocal calculus of variations- an illustration
- 3.5 Nonlocal calculus of variations- further discussions
- 3.6 Summary
- References
- 4 Local Limits and Asymptotically Compatible Discretizations.
- 4.1 Introduction
- 4.2 Local PDE limits of linear peridynamic models
- 4.3 Discretization schemes and discrete local limits
- 4.4 Asymptotically compatible schemes for peridynamics
- 4.5 Summary
- References
- 5 Roadmap for Software Implementation
- 5.1 Introduction
- 5.2 Evaluating the internal force density
- 5.3 Bond damage and failure
- 5.4 The tangent stiffness matrix
- 5.5 Modeling contact
- 5.6 Meshfree discretizations for peridynamics
- 5.7 Proximity search for identification of pairwise interactions
- 5.8 Time integration
- 5.8.1 Explicit time integration for transient dynamics
- 5.8.2 Estimating the maximum stable time step
- 5.8.3 Implicit time integration for quasi-statics
- 5.9 Example simulations
- 5.9.1 Fragmentation of a brittle disk resulting from impact
- 5.9.2 Quasi-static simulation of a tensile test
- 5.10 Summary
- References
- III: Material Models and Links to Atomistic Models
- 6 Constitutive Modeling in Peridynamics
- 6.1 Introduction
- 6.2 Kinematics, momentum conservation, and terminology
- 6.3 Linear peridynamic isotropic solid
- 6.3.1 Plane elasticity
- 6.3.1.1 Plane stress
- 6.3.1.2 Plane strain
- 6.3.2 "Bond-based" theories as a special case
- 6.3.3 On the role of the influence function
- 6.3.4 Other elasticity theories
- 6.4 Finite Deformations
- 6.4.1 Invariants of peridynamic scalar-states
- 6.5 Correspondence models
- 6.5.1 Non-ordinary correspondence models for solid mechanics
- 6.5.2 Ordinary correspondence models for solid mechanics
- 6.6 Plasticity
- 6.6.1 Yield surface and flow rule
- 6.6.2 Loading/unloading and consistency
- 6.6.3 Discussion
- 6.7 Non-ordinary models
- 6.7.1 A non-ordinary beam model
- 6.7.2 A non-ordinary plate/shell model
- 6.7.3 Other non-ordinary models
- 6.8 Final Comments
- References
- 7 Links between Peridynamic and Atomistic Models.
- 7.1 Introduction
- 7.2 Molecular dynamics
- 7.3 A meshfree discretization of peridynamic models
- 7.4 Upscaling molecular dynamics to peridynamics
- 7.4.1 A one-dimensional nonlocal linear springs model*
- 7.4.2 A three-dimensional embedded-atom model(Omitted)
- 7.5 Computational speedup through upscaling
- 7.6 Concluding remarks
- References
- 8 Absorbing Boundary Conditions with Verification
- 8.1 Introduction
- 8.2 A PML for state-based peridynamics
- 8.2.1 Two-dimensional (2D), state-based peridynamics review
- 8.2.2 Auxiliary field formulation and PML application
- 8.2.3 Numerical examples
- 8.3 Verification of cone and center crack problems
- 8.3.1 Dimensional analysis of Hertzian cone crack development in brittle elastic solids
- 8.3.2 State-based verification of a cone crack
- 8.3.3 Bond-based verification of a center crack
- 8.4 Verification of an axisymmetric indentation problem
- 8.4.1 Formulation
- 8.4.2 Analytical verification
- References
- IV: Modeling Material Failure and Damage
- 9 Dynamic Brittle Fracture as an Upscaling of Unstable Mesoscopic Dynamics
- 9.1 Introduction
- 9.2 The macroscopic evolution of brittle fracture as a small horizon limit of mesoscopic dynamics
- 9.3 Dynamic instability and fracture initiation
- 9.4 Localization of dynamic instability in the small horizon-macroscopic limit
- 9.5 Free crack propagation in the small horizon-macroscopic limit
- 9.6 Summary
- References
- 10 Crack Branching in Dynamic Brittle Fracture
- 10.1 Introduction
- 10.2 A brief review of literature on crack branching
- 10.2.1 Theoretical models and experimental results on dynamic brittle fracture and crack branching
- 10.2.2 Computations of dynamic brittle fracture based on FEM
- 10.2.3 Dynamic brittle fracture results based on atomistic modeling.
- 10.2.4 Dynamic brittle fracture based on particle and lattice-based methods
- 10.2.5 Phase-field models in dynamic fracture
- 10.2.6 Results on dynamic brittle fracture from peridynamic models
- 10.3 Brief review of the bond-based peridynamic model
- 10.4 An accurate and efficient quadrature scheme
- 10.5 Peridynamic results for dynamic fracture and crack branching
- 10.5.1 Crack branching in soda-lime glass
- 10.5.1.1 Load case 1: stress on boundaries
- 10.5.1.2 Load case 2: stress on pre-crack surfaces
- 10.5.1.3 Load case 3: velocity boundary conditions
- 10.5.2 Crack branching in homalite
- 10.5.2.1 Load case 1: stress on boundaries
- 10.5.2.2 Load case 2: stress on pre-crack surfaces
- 10.5.2.3 Load case 3: velocity boundary conditions
- 10.5.3 Influence of sample geometry
- 10.5.3.1 Load case 1: stress on boundaries
- 10.5.3.2 Load case 2: stress on pre-crack surfaces
- 10.5.3.3 Load case 3: velocity boundary conditions
- 10.6 Discussion of crack branching results
- 10.7 Why do cracks branch?
- 10.8 The importance of nonlocal modeling in crack branching
- 10.9 Conclusions
- References
- 11 Relations between Peridynamic and Classical Cohesive Models
- 11.1 Introduction
- 11.2 Analytical PD-based normal cohesive law
- 11.2.1 Case 1- No bonds have reached critical stretch
- 11.2.2 Case 2- Bonds have exceeded the critical stretch
- 11.2.3 Numerical approximation of PD-based cohesive law
- 11.3 PD-based tangential cohesive law
- 11.3.1 Case 1- No bonds have reached critical stretch
- 11.3.2 Case 2- Bonds have exceeded the critical stretch
- 11.4 PD-based mixed-mode cohesive law
- 11.5 Conclusions
- References
- 12 Peridynamic Modeling of Fiber-reinforced Composites
- 12.1 Introduction
- 12.2 Peridynamic analysis of a lamina
- 12.3 Peridynamic analysis of a laminate
- 12.4 Numerical results
- 12.5 Conclusions.
- 12.6 Appendix A: PD material constants of a lamina
- 12.6.1 Simple shear
- 12.6.2 Uniaxial stretch in the fiber direction
- 12.6.3 Uniaxial stretch in the transverse direction
- 12.6.4 Biaxial stretch
- 12.7 Appendix B: Surface correction factors for a composite lamina
- 12.8 Appendix C: PD interlayer and shear bond constants of a laminate
- 12.9 Appendix D: Critical Stretch Values for Bond Constants
- References
- 13 Peridynamic Modeling of Impact and Fragmentation
- 13.1 Introduction
- 13.2 Convergence studies and damage models that influence the damage behavior
- 13.2.1 Damage-dependent critical bond strain
- 13.2.2 Critical bond strain dependence on compressive strains along other directions
- 13.2.3 Surface effect in impact problems
- 13.2.4 Convergence study for impact on a glass plate
- 13.3 Impact on a multilayered glass system
- 13.3.1 Model description
- 13.3.2 A comparison between FEM and peridynamics for the elastic response of a multilayered system to impact
- 13.4 Computational results for damage progression in the seven-layer glass system
- 13.4.1 Damage evolution for the cross section
- 13.4.2 Damage evolution in the first layer
- 13.4.3 Damage evolution in the second layer
- 13.4.4 Damage evolution in the fourth layer
- 13.4.5 Damage evolution in the seventh layer
- 13.5 Conclusions
- References
- V: Multiphysics and Multiscale Modeling
- 14 Coupling Local and Nonlocal Models
- 14.1 Introduction
- 14.2 Energy-based blending schemes
- 14.2.1 The Arlequin method
- 14.2.1.1 Description of the coupling model
- 14.2.1.2 A numerical example
- 14.2.2 The morphing method
- 14.2.2.1 Overview
- 14.2.2.2 Description of the morphing method
- 14.2.2.3 One-dimensional analysis of ghost forces
- 14.2.2.4 Numerical examples
- 14.3 Force-based blending schemes*.
- 14.3.1 Convergence of peridynamic models to classical models.