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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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Detaylı Bibliyografya
Yazar:	Bobaru, Florin
Diğer Yazarlar:	Foster, John T., Geubelle, Philippe H., Silling, Stewart A.
Materyal Türü:	e-Kitap
Dil:	İngilizce
Baskı/Yayın Bilgisi:	Milton : CRC Press LLC, 2016.
Edisyon:	1st ed.
Seri Bilgileri:	Advances in Applied Mathematics Series
Konular:	Mathematical models. Electronic books.
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.

Handbook of Peridynamic Modeling.

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