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E-raamat: Handbook of Peridynamic Modeling

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Edited by (University of Nebraska, Lincoln, USA), Edited by (Sandia National Laboratories, Albuquerque, New Mexico, USA), Edited by (University of Illinois, Urbana, USA), Edited by (Univeristy of Texas, San Antonio, USA)
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Handbook of Peridynamic ModelingSuurem pilt
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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 unguided modeling of crack propagation/fracture in brittle, quasi-brittle, and ductile materials; autonomous transition from continuous damage/fragmentation to fracture; modeling of long-range forces within a continuous body; and multiscale coupling in a consistent mathematical framework.

Arvustused

Editors Bobaru, Foster, Geubelle, and Silling present readers with a collection of academic and research perspectives toward a comprehensive guide to contemporary peridynamic modeling in a variety of applications. The editors have organized the sixteen selections that make up the main body of the text in five parts devoted to the need for nonlocal modeling and introduction toperidynamics; mathematics, numerics, and software tools of peridynamics; material models and links to atomsistic models; and other related subjects. Florin Bobaru is a faculty member of the University of Nebraska-Lincoln. John T. Foster is a faculty member of the University of Texas at Austin. Philippe H. Geubelle is a faculty member of the University of Illinois. Stewart A. Silling is with Sandia National Laboratories in New Mexico

~ProtoView, 2017

Foreword xv
Preface xvii
List of Figures xix
List of Tables xxxv
Contributors xxxvii
I The Need for Nonlocal Modeling and Introduction to Peridynamics 1(60)
1 Why Peridynamics?
3(22)
Stewart A. Silling
1.1 The mixed blessing of locality
3(4)
1.2 Origins of nonlocality in a model
1.2.1 Long-range forces
7(3)
1.2.2 Coarsening a fine-scale material system
10(2)
1.2.3 Smoothing of a heterogeneous material system
12(6)
1.3 Nonlocality at the macroscale
18(2)
1.4 The mixed blessing of nonlocality
20(1)
References
21(4)
2 Introduction to Peridynamics
25(36)
Stewart A. Silling
2.1 Equilibrium in terms of integral equations
26(2)
2.2 Material modeling
28(14)
2.2.1 Bond-based materials
28(2)
2.2.2 Relation between bond densities and flux
30(2)
2.2.3 Peridynamic states
32(3)
2.2.4 Ordinary state-based materials
35(2)
2.2.5 Correspondence materials
37(2)
2.2.6 Discrete particles as peridynamic bodies
39(1)
2.2.7 Setting the horizon
40(1)
2.2.8 Linearized peridynamics
41(1)
2.3 Plasticity
42(3)
2.3.1 Bond-based microplastic material
42(1)
2.3.2 LPS material with plasticity
43(2)
2.4 Damage and fracture
45(6)
2.4.1 Damage in bond-based models
45(2)
2.4.2 Damage in ordinary state-based material models
47(2)
2.4.3 Damage in correspondence material models
49(1)
2.4.4 Nucleation strain
50(1)
2.5 Treatment of boundaries and interfaces
51(3)
2.5.1 Bond-based materials
51(2)
2.5.2 State-based materials
53(1)
2.6 Emu numerical method
54(2)
2.7 Conclusions
56(1)
References
57(4)
II Mathematics, Numerics, and Software Tools of Peridynamics 61(80)
3 Nonlocal Calculus of Variations and Well-Posedness of Peridynamics
63(24)
Qiang Du
3.1 Introduction
63(3)
3.2 A brief review of well-posedness results
66(1)
3.3 Nonlocal balance laws and nonlocal vector calculus
67(5)
3.4 Nonlocal calculus of variations - an illustration
72(7)
3.5 Nonlocal calculus of variations - further discussions
79(2)
3.6 Summary
81(1)
References
82(5)
4 Local Limits and Asymptotically Compatible Discretizations
87(22)
Qiang Du
4.1 Introduction
87(3)
4.2 Local PDE limits of linear peridynamic models
90(7)
4.3 Discretization schemes and discrete local limits
97(3)
4.4 Asymptotically compatible schemes for peridynamics
100(3)
4.5 Summary
103(1)
References
104(5)
5 Roadmap for Software Implementation
109(32)
David Littlewood
5.1 Introduction
109(3)
5.2 Evaluating the internal force density
112(3)
5.3 Bond damage and failure
115(1)
5.4 The tangent stiffness matrix
115(4)
5.5 Modeling contact
119(3)
5.6 Meshfree discretizations for peridynamics
122(2)
5.7 Proximity search for identification of pairwise interactions
124(1)
5.8 Time integration
125(6)
5.8.1 Explicit time integration for transient dynamics
126(2)
5.8.2 Estimating the maximum stable time step
128(1)
5.8.3 Implicit time integration for quasi-statics
129(2)
5.9 Example simulations
131(3)
5.9.1 Fragmentation of a brittle disk resulting from impact
131(2)
5.9.2 Quasi-static simulation of a tensile test
133(1)
5.10 Summary
134(2)
References
136(5)
III Material Models and Links to Atomistic Models 141(86)
6 Constitutive Modeling in Peridynamics
143(36)
John T. Foster
6.1 Introduction
144(2)
6.2 Kinematics, momentum conservation, and terminology
146(4)
6.3 Linear peridynamic isotropic solid
150(9)
6.3.1 Plane elasticity
152(1)
6.3.1.1 Plane stress
153(1)
6.3.1.2 Plane strain
156(1)
6.3.2 "Bond-based" theories as a special case
156(2)
6.3.3 On the role of the influence function
158(1)
6.3.4 Other elasticity theories
159(1)
6.4 Finite Deformations
159(4)
6.4.1 Invariants of peridynamic scalar-states
162(1)
6.5 Correspondence models
163(3)
6.5.1 Non-ordinary correspondence models for solid mechanics
164(1)
6.5.2 Ordinary correspondence models for solid mechanics
165(1)
6.6 Plasticity
166(3)
6.6.1 Yield surface and flow rule
167(1)
6.6.2 Loading/unloading and consistency
167(1)
6.6.3 Discussion
168(1)
6.7 Non-ordinary models
169(3)
6.7.1 A non-ordinary beam model
169(2)
6.7.2 A non-ordinary plate/shell model
171(1)
6.7.3 Other non-ordinary models
171(1)
6.8 Final Comments
172(1)
References
173(6)
7 Links between Peridynamic and Atomistic Models
179(22)
Pablo Seleson
Michael L. Parks
7.1 Introduction
179(2)
7.2 Molecular dynamics
181(1)
7.3 A meshfree discretization of peridynamic models
182(2)
7.4 Upscaling molecular dynamics to peridynamics
184(10)
7.4.1 A one-dimensional nonlocal linear springs model
184(5)
7.4.2 A tbree-dimensional embedded-atom model
189(5)
7.5 Computational speedup through upscaling
194(2)
7.6 Concluding remarks
196(1)
References
197(4)
8 Absorbing Boundary Conditions with Verification
201(26)
Raymond A. Wildman
George A. Gazonas
8.1 Introduction
201(1)
8.2 A PML for state-based peridynamics
202(11)
8.2.1 Two-dimensional (2D), state-based peridynamics review
202(2)
8.2.2 Auxiliary field formulation and PML application
204(6)
8.2.3 Numerical examples
210(3)
8.3 Verification of cone and center crack problems
213(6)
8.3.1 Dimensional analysis of Hertzian cone crack development in brittle elastic solids
213(3)
8.3.2 State-based verification of a cone crack
216(2)
8.3.3 Bond-based verification of a center crack
218(1)
8.4 Verification of an axisymmetric indentation problem
219(3)
8.4.1 Formulation
220(1)
8.4.2 Analytical verification
221(1)
References
222(5)
IV Modeling Material Failure and Damage 227(178)
9 Dynamic Brittle Fracture as an Upscaling of Unstable Mesoscopic Dynamics
229(16)
Robert P. Lipton
9.1 Introduction
229(5)
9.2 The macroscopic evolution of brittle fracture as a small horizon limit of mesoscopic dynamics
234(4)
9.3 Dynamic instability and fracture initiation
238(2)
9.4 Localization of dynamic instability in the small horizon-macroscopic limit
240(1)
9.5 Free crack propagation in the small horizon-macroscopic limit
241(1)
9.6 Summary
242(1)
References
243(2)
10 Crack Branching in Dynamic Brittle Fracture
245(72)
Florin Bobaru
Guanfeng Zhang
10.1 Introduction
246(3)
10.2 A brief review of literature on crack branching
249(7)
10.2.1 Theoretical models and experimental results on dynamic brittle fracture and crack branching
249(2)
10.2.2 Computations of dynamic brittle fracture based on FEM
251(2)
10.2.3 Dynamic brittle fracture results based on atomistic modeling
253(1)
10.2.4 Dynamic brittle fracture based on particle and lattice-based methods
253(1)
10.2.5 Phase-field models in dynamic fracture
254(1)
10.2.6 Results on dynamic brittle fracture from peridynamic models
255(1)
10.3 Brief review of the bond-based peridynamic model
256(4)
10.4 An accurate and efficient quadrature scheme
260(2)
10.5 Peridynamic results for dynamic fracture and crack branching
262(29)
10.5.1 Crack branching in soda-lime glass
265(1)
10.5.1.1 Load case 1: stress on boundaries
265(1)
10.5.1.2 Load case 2: stress on pre-crack surfaces
269(1)
10.5.1.3 Load case 3: velocity boundary conditions
272(3)
10.5.2 Crack branching in homalite
275(1)
10.5.2.1 Load case 1: stress on boundaries
276(1)
10.5.2.2 Load case 2: stress on pre-crack surfaces
278(1)
10.5.2.3 Load case 3: velocity boundary conditions
282(3)
10.5.3 Influence of sample geometry
285(1)
10.5.3.1 Load case 1: stress on boundaries
285(1)
10.5.3.2 Load case 2: stress on pre-crack surfaces
287(1)
10.5.3.3 Load case 3: velocity boundary conditions
289(2)
10.6 Discussion of crack branching results
291(5)
10.7 Why do cracks branch?
296(8)
10.8 The importance of nonlocal modeling in- crack branching
304(3)
10.9 Conclusions
307(2)
References
309(8)
11 Relations between Peridynamic and Classical Cohesive Models
317(22)
Scot M. Breitenfeld
Philippe H. Geubelle
Olaf Weckner
Stewart A. Silling
11.1 Introduction
317(2)
11.2 Analytical PD-based normal cohesive law
319(10)
11.2.1 Case 1 - No bonds have reached critical stretch
322(1)
11.2.2 Case 2 - Bonds have exceeded the critical stretch
323(2)
11.2.3 Numerical approximation of PD-based cohesive law
325(4)
11.3 PD-based tangential cohesive law
329(4)
11.3.1 Case 1 - No bonds have reached critical stretch
331(1)
11.3.2 Case 2 - Bonds have exceeded the critical stretch
331(2)
11.4 PD-based mixed-mode cohesive law
333(3)
11.5 Conclusions
336(1)
References
337(2)
12 Peridynamic Modeling of Fiber-reinforced Composites
339(40)
Erdogan Madenci
Erkan Oterkus
12.1 Introduction
339(2)
12.2 Peridynamic analysis of a lamina
341(6)
12.3 Peridynamic analysis of a laminate
347(2)
12.4 Numerical results
349(5)
12.5 Conclusions
354(1)
12.6 Appendix A: PD material constants of a lamina
354(9)
12.6.1 Simple shear
355(1)
12.6.2 Uniaxial stretch in the fiber direction
356(2)
12.6.3 Uniaxial stretch in the transverse direction
358(1)
12.6.4 Biaxial stretch
359(4)
12.7 Appendix B: Surface correction factors for a composite lamina
363(5)
12.8 Appendix C: PD interlayer and shear bond constants of a laminate
368(6)
12.9 Appendix D: Critical Stretch Values for Bond Constants
374(2)
References
376(3)
13 Peridynamic Modeling of Impact and Fragmentation
379(26)
Florin Bobaru
Zhanping Xu
Yenan Wang
13.1 Introduction
380(2)
13.2 Convergence studies and damage models that influence the damage behavior
382(6)
13.2.1 Damage-dependent critical bond strain
382(1)
13.2.2 Critical bond strain dependence on compressive strains along other directions
383(1)
13.2.3 Surface effect in impact problems
383(1)
13.2.4 Convergence study for impact on a glass plate
384(4)
13.3 Impact on a multilayered glass system
388(5)
13.3.1 Model description
389(2)
13.3.2 A comparison between FEM and peridynamics for the elastic response of a multilayered system to impact
391(2)
13.4 Computational results for damage progression in the seven-layer glass system
393(9)
13.4.1 Damage evolution for the cross section
394(2)
13.4.2 Damage evolution in the first layer
396(2)
13.4.3 Damage evolution in the second layer
398(1)
13.4.4 Damage evolution in the fourth layer
399(1)
13.4.5 Damage evolution in the seventh layer
400(2)
13.5 Conclusions
402(1)
References
403(2)
V Multiphysics and Multiscale Modeling 405(126)
14 Coupling Local and Nonlocal Models
407(30)
Yan Azdoud
Fei Han
David J. Littlewood
Gilles Lubineau
Pablo Seleson
14.1 Introduction
408(2)
14.2 Energy-based blending schemes
410(13)
14.2.1 The Arlequin method
410(1)
14.2.1.1 Description of the coupling model
410(1)
14.2.1.2 A numerical example
413(2)
14.2.2 The morphing method
415(1)
14.2.2.1 Overview
415(1)
14.2.2.2 Description of the morphing method
417(1)
14.2.2.3 One-dimensional analysis of ghost forces
419(1)
14.2.2.4 Numerical examples
419(4)
14.3 Force-based blending schemes
423(8)
14.3.1 Convergence of peridynamic models to classical models
424(1)
14.3.2 Derivation of force-based blending schemes
425(2)
14.3.3 A numerical example
427(4)
14.4 Summary
431(1)
References
431(6)
15 A Peridynamic Model for Corrosion Damage
437(52)
Ziguang Chen
Florin Bobaru
15.1 Introduction
438(5)
15.2 Electrochemical kinetics
443(3)
15.3 Problem formulation of 1D pitting corrosion
446(3)
15.4 The peridynamic formulation for 1D pitting corrosion
449(4)
15.5 Results and discussion of 1D pitting corrosion
453(6)
15.5.1 Pit corrosion depth proportional to
453(3)
15.5.2 Activation-controlled, diffusion-controlled, and IR-controlled corrosion
456(3)
15.6 Corrosion damage and the Concentration-Dependent Damage (CDD) model
459(6)
15.6.1 Damage evolution
462(2)
15.6.2 Saturated concentration
464(1)
15.7 Formulation and results of 2D and 3D pitting corrosion
465(11)
15.7.1 PD formulation of 2D and 3D pitting corrosion
466(3)
15.7.2 The Concentration-Dependent Damage (CDD) model for pitting corrosion: example in 2D
469(3)
15.7.3 A coupled corrosion/damage model for pitting corrosion: 2D example
472(2)
15.7.4 Diffusivity affects the corrosion rate
474(1)
15.7.5 Pitting corrosion with the CDD+DDC model in 3D
475(1)
15.8 Pitting corrosion in heterogeneous materials: examples in 2D
476(4)
15.8.1 Pitting corrosion in layer structures
476(3)
15.8.2 Pitting corrosion in a material with inclusions: a 2D example
479(1)
15.9 Conclusions
480(1)
15.10 Appendix
481(3)
15.10.1 Convergence study for 1D diffusion-controlled corrosion
481(1)
15.10.2 Convergence study for 2D activation-controlled corrosion with Concentration-Dependent Damage model
482(2)
References
484(5)
16 Peridynamics for Coupled Field Equations
489(42)
Erdogan Madenci
Selda Oterkus
16.1 Introduction
490(2)
16.2 Diffusion equation
492(2)
16.2.1 Thermal diffusion
492(1)
16.2.2 Moisture diffusion
493(1)
16.2.3 Electrical conduction
493(1)
16.3 Coupled field equations
494(6)
16.3.1 Thermomechanics
494(1)
16.3.1.1 Thermal diffusion with a structural coupling term
494(1)
16.3.1.2 Equation of motion with a thermal coupling term
495(1)
16.3.2 Porelasticity
495(1)
16.3.2.1 Mechanical deformation due to fluid pressure
495(1)
16.3.2.2 Fluid flow in porous medium
496(1)
16.3.3 Electromigration
497(2)
16.3.4 Hygrothermomechanics
499(1)
16.4 Numerical solution to peridynamic field equations
500(11)
16.4.1 Correction of PD material parameters
500(2)
16.4.2 Boundary conditions
502(1)
16.4.2.1 Essential boundary conditions
502(1)
16.4.2.2 Natural boundary conditions
503(1)
16.4.2.3 Example 1
506(1)
16.4.2.4 Example 2
507(1)
16.4.2.5 Example 3
509(2)
16.5 Applications
511(16)
16.5.1 Coupled nonuniform heating and deformation
511(3)
16.5.2 Coupled nonuniform moisture and deformation in a square plate
514(5)
16.5.3 Coupled fluid pore pressure and deformation
519(5)
16.5.4 Coupled electrical, temperature, deformation, and vacancy diffusion
524(3)
16.6 Remarks
527(1)
References
528(3)
Index 531
Bobaru, Florin; Foster, John T.; Geubelle, Philippe H; Silling, Stewart A.
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