Peridynamic Modeling, Numerical Techniques, and Applications

✍ Scribed by Erkan Oterkus, Selda Oterkus, Erdogan Madenci

• Publisher: Elsevier
• Year: 2021
• Tongue: English
• Leaves: 438
• Series: Elsevier Series in Mechanics of Advanced Materials
• Category: Library

✦ Synopsis

This book provides readers with an incisive look at cutting-edge peridynamic modeling methods, numerical techniques, their applications, and potential future directions for the field. It starts with an introductory chapter authored by Stewart Silling, who originally developed peridynamics. It then looks at new concepts in the field, with chapters covering dual-horizon peridynamics, peridynamics for axisymmetric analysis, beam and plate models in peridynamics, coupled peridynamics and XFEM, peridynamics for dynamic fracture modeling, and more. From there, it segues into coverage of cutting-edge applications of peridynamics, exploring its biological applications, modeling at the nanoscale, peridynamics for composites delamination and damage in ceramics, and more, concluding with a chapter on the application of artificial intelligence and machine learning in peridynamics.

✦ Table of Contents

Mechanics-of-Advanced-Materi_2021_Peridynamic-Modeling--Numerical-Techniques
Mechanics of Advanced Materials Series
Series editor-in-chief: Vadim V. Silberschmidt
Series editor: Thomas Böhlke
Series editor: David L. McDowell
Series editor: Zhong Chen
Front-Matter_2021_Peridynamic-Modeling--Numerical-Techniques--and-Applicatio
Peridynamic Modeling, Numerical Techniques, and ApplicationsELSEVIER SERIES IN MECHANICS OF ADVANCED MATERIALSEdited byErka ...
Copyright_2021_Peridynamic-Modeling--Numerical-Techniques--and-Applications
Copyright
Contributors_2021_Peridynamic-Modeling--Numerical-Techniques--and-Applicatio
Contributors
Preface_2021_Peridynamic-Modeling--Numerical-Techniques--and-Applications
Preface
Chapter-1---Introduc_2021_Peridynamic-Modeling--Numerical-Techniques--and-Ap
1 . Introduction
1. What is peridynamics?
2. Peridynamics obtained from the smoothing of an atomic system
3. Material models
3.1 Linear microelastic model
3.2 Prototype microelastic brittle model
3.3 Microelastic nucleation and growth model
3.4 Nonlinear and rate-dependent bond-based models
3.5 Ordinary state-based material models
3.6 Non-ordinary state-based materials and the correspondence model
4. Relation to the local theory
5. Simple meshless discretization
6. Some research trends in the peridynamic theory
6.1 Special purpose material models
6.2 Wave dispersion
6.3 Material stability
6.4 Micropolar theories
6.5 Better meshless numerical techniques
6.6 Ductile material response
6.7 Multiple physical fields
6.8 Material variability
7. Conclusions
Acknowledgments
References
Chapter-2---Dual-horizon-perid_2021_Peridynamic-Modeling--Numerical-Techniqu
2 . Dual-horizon peridynamics (DH-PD)
1. Introduction
2. Ghost force in traditional peridynamics
3. Dual-horizon concept
4. Forces in dual-horizon peridynamics
5. Equation of motion in dual-horizon peridynamics
6. Test of spurious wave
7. Adaptivity and particles arrangement sensitivity
7.1 Kalthoff-Winkler test in 2D and 3D
7.2 Hydraulic fracturing
8. Weak continuity along the materials interfaces
8.1 1D bimaterial bar under tension
8.2 Crack propagation in heterogeneous materials
9. Conclusion and discussion
Acknowledgments
References
Chapter-3---Peridynamics-for-axi_2021_Peridynamic-Modeling--Numerical-Techni
3 . Peridynamics for axisymmetric analysis
1. Introduction
2. Classical axisymmetric equilibrium equations
3. Peridynamic theory
4. Weak form of PD equation of motion
5. Failure criteria
6. Numerical results
6.1 A cylindrical body with or without an internal ring crack under tension
7. Conclusions
References
Chapter-4---Peridynamics-damage-model_2021_Peridynamic-Modeling--Numerical-T
4 . Peridynamics damage model through phase field theory
1. Introduction
2. Phase field theory: A brief recap
3. PD reformulation of phase field theory
3.1 Kinematics
3.2 Governing equations
3.3 Kinematic correspondence
3.4 Constitutive correspondence
3.5 Equations in an explicit form
4. Criterion for bond breaking
5. Numerical illustrations
5.1 Dynamic crack branching
5.2 Simulation of Kalthoff-Winkler experiment
6. Concluding remarks
References
Chapter-5---Beam-and-plate-model_2021_Peridynamic-Modeling--Numerical-Techni
5 . Beam and plate models in peridynamics
1. Introduction
2. Peridynamic Timoshenko beam formulation
2.1 Classical Timoshenko beam formulation
2.2 Peridynamic Timoshenko beam formulation
3. Peridynamic Mindlin plate formulation
3.1 Classical Mindlin plate formulation
3.2 Peridynamic Mindlin plate formulation
4. Numerical results
4.1 Simply supported beam subjected to transverse loading
4.2 Mindlin plate subjected to simply supported boundary conditions
5. Conclusions
References
Chapter-6---Coupling-of-CCM-and-P_2021_Peridynamic-Modeling--Numerical-Techn
6 . Coupling of CCM and PD in a meshless way
1. Introduction
2. The splice method, at a continuum level
2.1 Peridynamics formulation
2.2 Splice between a PD region and a CCM region
3. A meshless discretisation of CCM: the finite point method
4. A meshless discretisation of PD
5. Details on the discretised version of the coupling
6. Numerical examples
6.1 Example 1: pre-cracked plate subjected to traction
6.2 Example 2: Kalthoff-Winkler experiment
7. Conclusions
Acknowledgments
References
Chapter-7---Coupled-peridynam_2021_Peridynamic-Modeling--Numerical-Technique
7 . Coupled peridynamics and XFEM
1. Introduction
2. Peridynamic differential operator
3. XFEM in conjunction with peridynamics
3.1 Displacements at peridynamic material points
3.2 Principle of virtual work
4. Activation of enrichment functions
5. Numerical results
5.1 Plate with a straight crack under tension
5.2 Plate with an inclined crack under tension
6. Conclusions
References
Chapter-8---Peridynamics-in-dynam_2021_Peridynamic-Modeling--Numerical-Techn
8 . Peridynamics in dynamic fracture modeling
1. Introduction
2. Ordinary state-based peridynamics
2.1 Discretization of peridynamic formulation
3. Fracture modeling
3.1 Interaction integrals
3.1.1 Interaction integral for stationary cracks
3.1.2 Interaction integral for propagating cracks
3.2 MLS approximation
4. Evaluation of mixed-mode DSIFs for stationary cracks
5. Dynamic crack propagation and arrest modeling
5.1 Transition bond modeling
5.2 Crack arrest modeling with application phase
5.3 Numerical studies
6. Concluding remarks
References
Chapter-9---Contact-analysis-of-rigid-an_2021_Peridynamic-Modeling--Numerica
9 . Contact analysis of rigid and deformable bodies with peridynamics
1. Introduction
2. Approach
2.1 Bond-based peridynamic model
2.2 Rigid impactor model
3. Contact model between the impactor and target
4. Numerical results
4.1 Normal impact of a rigid sphere (single sub-volume) on a simply supported plate
4.2 Normal impact of a rigid sphere (multiple sub-volume) on a fully clamped plate
5. Conclusions
References
Chapter-10---Modeling-inelastici_2021_Peridynamic-Modeling--Numerical-Techni
10 . Modeling inelasticity in peridynamics
1. Introduction
2. Peridynamic plasticity formulation
3. Peridynamic viscoelasticity formulation
4. Numerical results
4.1 Plate under tensile loading
4.2 Plate with a pre-existing crack under tensile loading
5. Conclusions
References
Chapter-11---Kinematically-exa_2021_Peridynamic-Modeling--Numerical-Techniqu
11 . Kinematically exact peridynamics
1. Introduction
2. Kinematics
3. Governing equations
3.1 Internal potential energy
3.1.1 One-neighbor interactions
3.1.2 Two-neighbor interactions
3.1.3 Three-neighbor interactions
3.2 External potential energy
3.3 Equilibrium
4. Computational implementation
5. Harmonic potentials
6. Examples
7. Conclusion
References
Chapter-12---Modeling-biological-ma_2021_Peridynamic-Modeling--Numerical-Tec
12 . Modeling biological materials with peridynamics
1. Introduction
2. Methodology
2.1 Background and notation
2.2 Implementing growth and remodeling
2.3 Note on emergent behavior
3. Example applications
3.1 Fracture in biological materials
3.2 Tissue growth and shrinkage
3.2.1 Cell division and tissue growth
3.2.2 Cell death and tissue shrinkage
3.3 Connecting emergent behavior across scales
4. Conclusion and outlook
Acknowledgments
References
Chapter-13---The-application-of-peri_2021_Peridynamic-Modeling--Numerical-Te
13 . The application of peridynamics for ice modeling
1. Introduction
1.1 Structure and properties of ice
1.1.1 Structure of natural ice
1.1.2 Mechanical properties
1.2 Constitutive for ice
1.2.1 Elastic-brittle constitutive
1.2.2 Ductile constitutive
1.2.3 Ductile-brittle transition
1.3 Advantages and research status of using peridynamics to study ice
1.3.1 Advantages
1.3.2 Research status
2. Numerical study of mechanical properties of ice
2.1 Pre-crack propagation under tension of 2D flat ice
2.2 Wing crack propagation in 3D ice body
2.3 Three-point bending test of ice
2.4 Ice impacting on reinforced plate structure
2.5 The interaction between ice and cylindrical structure
3. Numerical simulation of interaction between level ice and sloping structure
3.1 Numerical model
3.1.1 Contact
3.1.2 Buoyancy
3.2 2D numerical analysis of interaction between ice and sloping structure
3.2.1 Numerical results
3.2.2 Influence factors of damage of ice
3.3 3D numerical analysis of interaction between ice and sloping structure
4. Research on numerical simulation of ice breaking by underwater explosion based on BBPD method
4.1 Explosive load
4.2 Numerical modeling and analysis
5. Numerical simulation of continuous icebreaking based on hybrid modeling method
5.1 Calculation model
5.2 Numerical results
References
Further reading
Chapter-14---Fiber-reinforced-composit_2021_Peridynamic-Modeling--Numerical-
14 . Fiber-reinforced composites modeling using peridynamics
1. Introduction
2. Peridynamics for composite materials
2.1 Theoretical background
2.2 Two different versions of PD model for composite ply
Model (a): Oterkus-Madenci's ply model including fiber and matrix bonds
Model (b): Ghajari-Iannucci-Curtis' ply model using continuous function of bond constants
2.3 Interlaminar bond and failure model
3. Numerical examples
3.1 Modeling of curvilinear fiber path
3.2 Multiple-site, multiple-type damage in laminated composites
3.3 Integrated framework for manufacturing and design of composites
4. Conclusions and future outlook
Acknowledgments
References
Chapter-15---Phase-field-based-peridynamics-damage_2021_Peridynamic-Modeling
15 . Phase field–based peridynamics damage model: Applications to delamination of composite structures and inelastic response of ...
1. Introduction
2. Review of cohesive zone model (CZM) and Deshpande-Evans (DE) model
2.1 Cohesive zone model (CZM)
2.2 Deshpande-Evans (DE) constitutive model
3. Phase field–based PD damage model for composites delamination
3.1 Governing equations
3.2 Bulk and interface constitutive models
4. Numerical illustrations on composites delamination
4.1 Mode I delamination
4.2 Mode II delamination
4.2.1 End loaded split test
4.2.2 End notched flexure test
4.3 Mixed (I/II) mode delamination
4.3.1 Fixed ratio mixed-mode test
5. DE damage model using phase field–based PD
5.1 Phase field–based PD damage formulation using complementary energy density
5.2 Rate of internal energy density
5.3 Equations of motion for spherically symmetric geometry and loading
5.3.1 Constitutive correspondence
6. Numerical illustrations
7. Concluding remarks
References
Chapter-16---Peridynamic-modeli_2021_Peridynamic-Modeling--Numerical-Techniq
16 . Peridynamic modeling at nano-scale
1. Introduction
2. PD model for the failure of SLGS
2.1 Original PD formulation
2.2 PD model of SLGS
2.2.1 Establishment of the PD model
2.2.2 Determination of the PD parameters
3. PD simulation of the failure of SLGS
3.1 A CG idea for SLGS
3.2 Failure of SLGS
3.2.1 Validation of the PD model of SLGS
3.2.2 Failure modes of different SLGS
3.3 Discussion
4. Conclusion
References
Chapter-17---Multiscale-modeling_2021_Peridynamic-Modeling--Numerical-Techni
17 . Multiscale modeling with peridynamics
1. Introduction
2. Coarsening approach
2.1 Coarsening of peridynamic model
2.2 Numerical implementation
2.3 Coarsening the micromodulus function
2.3.1 Coarsening of 1D micromodulus function
2.3.2 Coarsening of two-dimensional micromodulus functions
3. Model order reduction using static condensation
3.1 Reduced dynamic and static models
3.2 Reduced eigenvalue models
4. Homogenization approach
5. Conclusions
References
Chapter-18---Application-of-peridynamics_2021_Peridynamic-Modeling--Numerica
18 . Application of peridynamics for rock mechanics and porous media
1. Introduction
2. Fully coupled poroelastic peridynamic formulation
3. Numerical implementation
4. Numerical results
4.1 Consolidation problem (1D)
4.2 Consolidation problem (2D)
4.3 Square plate with a hydraulically pressurized crack problem (2D)
5. Conclusions
References
Further reading
Chapter-19---Application-of-high-perfo_2021_Peridynamic-Modeling--Numerical-
19 . Application of high-performance computing for peridynamics
1. Introduction
2. Parallel programming of a PD code
2.1 CPU-based approach
Export OMP_NUM_THREADS=8
2.2 GPU-based approach
3. Numerical results
4. Conclusions
References
Chapter-20---Application-of-artificial-int_2021_Peridynamic-Modeling--Numeri
20 . Application of artificial intelligence and machine learning in peridynamics
1. Introduction
2. Linear regression
3. One-dimensional peridynamic machine learning formulation
4. Two-dimensional peridynamic machine learning formulation
5. Numerical results
5.1 One-dimensional bar subjected to axial loading
5.2 Vibration of a one-dimensional bar
5.3 Two-dimensional plate subjected to tension loading
5.4 Two-dimensional plate with a pre-existing crack subjected to tension loading
6. Conclusions
References
Index_2021_Peridynamic-Modeling--Numerical-Techniques--and-Applications
Index
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K
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Q
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