| Description |
1 online resource (587 pages) |
| Series |
Advances in Applied Mathematics |
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Advances in applied mathematics.
|
| Contents |
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 |
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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 |
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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 |
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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 |
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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 |
| Summary |
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 |
| Notes |
3 Nonlocal Calculus of Variations and Well-Posedness of Peridynamics |
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Print version record |
| Subject |
Mathematical models.
|
|
Models, Theoretical
|
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mathematical models.
|
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Mathematical models
|
| Form |
Electronic book
|
| Author |
Foster, John T
|
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Geubelle, Philippe H
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Silling, Stewart A
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| ISBN |
9781482230444 |
|
1482230445 |
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