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Size Effects and Material Length Scales in Nanoindentation for Metals Read chapter Read first chapter

2019 | OriginalPaper | Chapter

35. Recent Progress in Mathematical and Computational Aspects of Peridynamics

Authors : Marta D’Elia, Qiang Du, Max Gunzburger

Published in: Handbook of Nonlocal Continuum Mechanics for Materials and Structures

Publisher: Springer International Publishing

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Abstract

Recent developments in the mathematical and computational aspects of the nonlocal peridynamic model for material mechanics are provided. Based on a recently developed vector calculus for nonlocal operators, a mathematical framework is constructed that has proved useful for the mathematical analyses of peridynamic models and for the development of finite element discretizations of those models. A specific class of discretization algorithms referred to as asymptotically compatible schemes is discussed; this class consists of methods that converge to the proper limits as grid sizes and nonlocal effects tend to zero. Then, the multiscale nature of peridynamics is discussed including how, as a single model, it can account for phenomena occurring over a wide range of scales. The use of this feature of the model is shown to result in efficient finite element implementations. In addition, the mathematical and computational frameworks developed for peridynamic simulation problems are shown to extend to control, coefficient identification, and obstacle problems.

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previous chapter Peridynamics: Introduction
next chapter Optimization-Based Coupling of Local and Nonlocal Models: Applications to Peridynamics
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Metadata
Title
Recent Progress in Mathematical and Computational Aspects of Peridynamics
Authors
Marta D’Elia
Qiang Du
Max Gunzburger
Copyright Year
2019
Book
Handbook of Nonlocal Continuum Mechanics for Materials and Structures

Print ISBN: 978-3-319-58727-1

Electronic ISBN: 978-3-319-58729-5

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-319-58729-5_30

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