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

2019 | OriginalPaper | Chapter

34. Peridynamics: Introduction

Author : S. A. Silling

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

Publisher: Springer International Publishing

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Abstract

The peridynamic theory is a nonlocal extension of continuum mechanics that is compatible with the physical nature of cracks as discontinuities. It avoids the need to evaluate the partial derivatives of the deformation with respect to the spatial coordinates, instead using an integro-differential equation for the linear momentum balance. This chapter summarizes the peridynamic theory, emphasizing the continuum mechanical and thermodynamic aspects. Formulation of material models is discussed, including details on the statement of models using mathematical objects called peridynamic states that are nonlocal and nonlinear generalizations of second-order tensors. Damage evolution is treated within a nonlocal thermodynamic framework making use of the dependence of free energy on damage. Continuous, stable growth of damage can suddenly become unstable, leading to dynamic fracture. Peridynamics treats fracture and long-range forces on the same mathematical basis as continuous deformation and contact forces, extending the applicability of continuum mechanics to new classes of problems.

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Metadata
Title
Peridynamics: Introduction
Author
S. A. Silling
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_29

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