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Theory and application of Weibull distributions to 1D peridynamics for brittle solids

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Title: Theory and application of Weibull distributions to 1D peridynamics for brittle solids
Authors: Jones, LD
Vandeperre, LJ
Haynes, TA
Wenman, MR
Item Type: Journal Article
Abstract: Peridynamics is a continuum mechanics modelling method, which is emerging as a solution for – in particular – the modelling of brittle fracture. The inherent variability of brittle fracture is captured well by the Weibull distribution, which describes the probability of fracture of a given material at a given stress. Recreating a Weibull distribution in peridynamics involves adjusting for the fact that the body is made up of a large number of bonds, and the distribution of strengths associated with these bonds must be different to the distribution of strengths associated with the peridynamic body. In the local case, where the horizon ratio, m=1 is used, Weibull’s original simple size scaling gives exact results, but the overlapping nature of non-local bonds that occurs in higher m cases, typically used in the peridynamics literature (such as m=3), causes a significant distortion of Weibull distributions. The cause of these distortions is spurious toughening and partial component failures as a result of the reduced localisation associated with larger horizon ratios. In order to remove these distortions, appropriate size scaling is used for the bonds, and a methodology that is capable of reflecting the heterogeneity of the material in the model, is proposed. The methodology described means Weibull parameters measured at specimen or component level can be reproduced for higher values of m.
Issue Date: 1-May-2020
Date of Acceptance: 3-Feb-2020
URI: http://hdl.handle.net/10044/1/76918
DOI: 10.1016/j.cma.2020.112903
ISSN: 0045-7825
Publisher: Elsevier BV
Start Page: 1
End Page: 11
Journal / Book Title: Computer Methods in Applied Mechanics and Engineering
Volume: 363
Copyright Statement: © 2020 Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/
Sponsor/Funder: National Nuclear Laboratory (NNL)
Funder's Grant Number: PO 1015559
Keywords: 01 Mathematical Sciences
09 Engineering
Applied Mathematics
Publication Status: Published online
Article Number: 112903
Online Publication Date: 2020-02-13
Appears in Collections:Materials