An adaptive stochastic multi-scale method for cohesive fracture modelling of quasi-brittle heterogeneous materials under uniaxial tension

R. M. Sencu; Zhenjun Yang; Y. C. Wang

doi:10.1016/j.engfracmech.2016.02.040

An adaptive stochastic multi-scale method for cohesive fracture modelling of quasi-brittle heterogeneous materials under uniaxial tension

R. M. Sencu, Zhenjun Yang, Y. C. Wang

University of Manchester

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Abstract

An adaptive stochastic multi-scale method is developed for cohesive fracture modelling of quasi-brittle heterogeneous materials under uniaxial tension. In this method, a macro-domain is first discretised into a number of non-overlapping meso-scale elements (MeEs) each of which containing detailed micro-scale finite element meshes. Potential discrete cracks in the MeEs are modelled by pre-inserted cohesive interface elements (CIEs). Nonlinear simulations are conducted for the MeEs to obtain the crack patterns under different boundary conditions. The macro-domain with the same number of overlapped, adaptively size-increasing MeEs are then simulated, until the potential cracks seamlessly cross the boundaries of adjacent MeEs. The resultant cracks, after being filtered by a new Bayesian inference algorithm to remove spurious cracks wherever necessary, are then integrated as CIEs into a final anisotropic macro-model for global mechanical responses. A two-dimensional example of carbon fibre reinforced polymers was modelled under two types of uniaxial tension boundaries. The developed method predicted crack patterns and load-displacement curves in excellent agreement with those from a full micro-scale simulation, but consuming considerably less computation time of the latter.

Original language	English
Pages (from-to)	499–522
Number of pages	24
Journal	Engineering Fracture Mechanics
Volume	163
Early online date	16 Apr 2016
DOIs	https://doi.org/10.1016/j.engfracmech.2016.02.040
Publication status	Published - 16 Sept 2016

Bibliographical note

Publisher Statement: NOTICE: this is the author’s version of a work that was accepted for publication in Engineering Fracture Mechanics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Engineering Fracture Mechanics, [163, (2016)] DOI: 10.1016/j.engfracmech.2016.02.040

© 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
http://creativecommons.org/licenses/by-nc-nd/4.0/
NOTICE: this is the author’s version of a work that was accepted for publication in Engineering Fracture Mechanics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Engineering Fracture Mechanics, VOL 163, 2016, 10.1016/j.engfracmech.2016.02.040: 10.1016/j.engfracmech.2016.02.040

© 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

Multi-scale stochastic fracture mechanics
Scale coupling
Cohesive crack model
Overlapping elements
Fibre reinforced plastics

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10.1016/j.engfracmech.2016.02.040

Post-PrintAccepted author manuscript, 5.07 MBLicence: CC BY-NC-ND

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title = "An adaptive stochastic multi-scale method for cohesive fracture modelling of quasi-brittle heterogeneous materials under uniaxial tension",

abstract = "An adaptive stochastic multi-scale method is developed for cohesive fracture modelling of quasi-brittle heterogeneous materials under uniaxial tension. In this method, a macro-domain is first discretised into a number of non-overlapping meso-scale elements (MeEs) each of which containing detailed micro-scale finite element meshes. Potential discrete cracks in the MeEs are modelled by pre-inserted cohesive interface elements (CIEs). Nonlinear simulations are conducted for the MeEs to obtain the crack patterns under different boundary conditions. The macro-domain with the same number of overlapped, adaptively size-increasing MeEs are then simulated, until the potential cracks seamlessly cross the boundaries of adjacent MeEs. The resultant cracks, after being filtered by a new Bayesian inference algorithm to remove spurious cracks wherever necessary, are then integrated as CIEs into a final anisotropic macro-model for global mechanical responses. A two-dimensional example of carbon fibre reinforced polymers was modelled under two types of uniaxial tension boundaries. The developed method predicted crack patterns and load-displacement curves in excellent agreement with those from a full micro-scale simulation, but consuming considerably less computation time of the latter.",

keywords = "Multi-scale stochastic fracture mechanics, Scale coupling, Cohesive crack model, Overlapping elements, Fibre reinforced plastics",

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note = "Publisher Statement: NOTICE: this is the author{\textquoteright}s version of a work that was accepted for publication in Engineering Fracture Mechanics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Engineering Fracture Mechanics, [163, (2016)] DOI: 10.1016/j.engfracmech.2016.02.040 {\textcopyright} 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ http://creativecommons.org/licenses/by-nc-nd/4.0/ NOTICE: this is the author{\textquoteright}s version of a work that was accepted for publication in Engineering Fracture Mechanics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Engineering Fracture Mechanics, VOL 163, 2016, 10.1016/j.engfracmech.2016.02.040: 10.1016/j.engfracmech.2016.02.040 {\textcopyright} 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ ",

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AU - Sencu, R. M.

AU - Yang, Zhenjun

AU - Wang, Y. C.

N1 - Publisher Statement: NOTICE: this is the author’s version of a work that was accepted for publication in Engineering Fracture Mechanics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Engineering Fracture Mechanics, [163, (2016)] DOI: 10.1016/j.engfracmech.2016.02.040 © 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ http://creativecommons.org/licenses/by-nc-nd/4.0/ NOTICE: this is the author’s version of a work that was accepted for publication in Engineering Fracture Mechanics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Engineering Fracture Mechanics, VOL 163, 2016, 10.1016/j.engfracmech.2016.02.040: 10.1016/j.engfracmech.2016.02.040 © 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/

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N2 - An adaptive stochastic multi-scale method is developed for cohesive fracture modelling of quasi-brittle heterogeneous materials under uniaxial tension. In this method, a macro-domain is first discretised into a number of non-overlapping meso-scale elements (MeEs) each of which containing detailed micro-scale finite element meshes. Potential discrete cracks in the MeEs are modelled by pre-inserted cohesive interface elements (CIEs). Nonlinear simulations are conducted for the MeEs to obtain the crack patterns under different boundary conditions. The macro-domain with the same number of overlapped, adaptively size-increasing MeEs are then simulated, until the potential cracks seamlessly cross the boundaries of adjacent MeEs. The resultant cracks, after being filtered by a new Bayesian inference algorithm to remove spurious cracks wherever necessary, are then integrated as CIEs into a final anisotropic macro-model for global mechanical responses. A two-dimensional example of carbon fibre reinforced polymers was modelled under two types of uniaxial tension boundaries. The developed method predicted crack patterns and load-displacement curves in excellent agreement with those from a full micro-scale simulation, but consuming considerably less computation time of the latter.

AB - An adaptive stochastic multi-scale method is developed for cohesive fracture modelling of quasi-brittle heterogeneous materials under uniaxial tension. In this method, a macro-domain is first discretised into a number of non-overlapping meso-scale elements (MeEs) each of which containing detailed micro-scale finite element meshes. Potential discrete cracks in the MeEs are modelled by pre-inserted cohesive interface elements (CIEs). Nonlinear simulations are conducted for the MeEs to obtain the crack patterns under different boundary conditions. The macro-domain with the same number of overlapped, adaptively size-increasing MeEs are then simulated, until the potential cracks seamlessly cross the boundaries of adjacent MeEs. The resultant cracks, after being filtered by a new Bayesian inference algorithm to remove spurious cracks wherever necessary, are then integrated as CIEs into a final anisotropic macro-model for global mechanical responses. A two-dimensional example of carbon fibre reinforced polymers was modelled under two types of uniaxial tension boundaries. The developed method predicted crack patterns and load-displacement curves in excellent agreement with those from a full micro-scale simulation, but consuming considerably less computation time of the latter.

KW - Multi-scale stochastic fracture mechanics

KW - Scale coupling

KW - Cohesive crack model

KW - Overlapping elements

KW - Fibre reinforced plastics

U2 - 10.1016/j.engfracmech.2016.02.040

DO - 10.1016/j.engfracmech.2016.02.040

M3 - Article

SN - 0013-7944

VL - 163

SP - 499

EP - 522

JO - Engineering Fracture Mechanics

JF - Engineering Fracture Mechanics

ER -

An adaptive stochastic multi-scale method for cohesive fracture modelling of quasi-brittle heterogeneous materials under uniaxial tension

Abstract

Bibliographical note

Keywords

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