On the computational derivation of bond-based peridynamic stress tensor
File(s)
Published version
Author(s)
Type
Journal Article
Abstract
The concept of ‘contact stress’, as introduced by Cauchy, is a special case of a nonlocal stress tensor. In this work, the nonlocal stress tensor is derived through implementation of the bond-based formulation of peridynamics that uses an idealised model of interaction between points as bonds. The method is sufficiently general and can be implemented to study stress states in problems containing stress concentration, singularity, or discontinuities. Two case studies are presented, to study stress concentration around a circular hole in a square plate and conventionally singular stress fields in the vicinity of a sharp crack tip. The peridynamic stress tensor is compared with finite element approximations and available analytical solutions. It is shown that peridynamics is capable of capturing both shear and direct stresses and the results obtained correlate well with those obtained using analytical solutions and finite element approximations. A built-in MATLAB code is developed and used to construct a 2D peridynamic grid and subsequently approximate the solution of the peridynamic equation of motion. The stress tensor is then obtained using the tensorial product of bond force projections for bonds that geometrically pass through the point. To evaluate the accuracy of the predicted stresses near a crack tip, the J-integral value is computed using both a direct contour approximation and the equivalent domain integral method. In the formulation of the contour approximation, bond forces are used directly while the proposed peridynamic stress tensor is used for the domain method. The J-integral values computed are compared with those obtained by the commercial finite element package Abaqus 2018. The comparison provides an indication on the accurate prediction of the state of stress near the crack tip.
Date Issued
2020-12
Date Acceptance
2020-06-05
Citation
Journal of Peridynamics and Nonlocal Modeling, 2020, 2, pp.352-378
ISSN
2522-896X
Publisher
Springer Science and Business Media LLC
Start Page
352
End Page
378
Journal / Book Title
Journal of Peridynamics and Nonlocal Modeling
Volume
2
Copyright Statement
© The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which
permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give
appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and
indicate if changes were made. The images or other third party material in this article are included in the article's
Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included
in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or
exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy
of this licence, visit http://creativecommons.org/licenses/by/4.0/.
permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give
appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and
indicate if changes were made. The images or other third party material in this article are included in the article's
Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included
in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or
exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy
of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Sponsor
EDF Energy Nuclear Generation Ltd
Identifier
https://link.springer.com/article/10.1007%2Fs42102-020-00036-9
Grant Number
4840365490
Publication Status
Published online
Date Publish Online
2020-07-02