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Publication type: Article in scientific journal
Type of review: Peer review (publication)
Title: On the computational derivation of bond-based peridynamic stress tensor
Authors: Soleiman Fallah, Arash
Giannakeas, Ilias N.
Mella, Rizgar
Wenman, Mark R.
Safa, Yasser
Bahai, Hamid
et. al: No
DOI: 10.1007/s42102-020-00036-9
Published in: Journal of Peridynamics and Nonlocal Modeling
Issue Date: 2-Jul-2020
Publisher / Ed. Institution: Springer
ISSN: 2522-8978
Language: English
Subjects: Peridynamics; Stress tensor; J-integral; Discontinuity; Singularity
Subject (DDC): 530: Physics
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 finite element package Abaqus 2018. The comparison provides an indication on the accurate prediction of the state of stress near the crack tip.
Fulltext version: Published version
License (according to publishing contract): CC BY 4.0: Attribution 4.0 International
Departement: School of Engineering
Organisational Unit: Institute of Computational Physics (ICP)
Appears in collections:Publikationen School of Engineering

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