A temporal averaging–based approach to toughness homogenisation in heterogeneous material

Gaspare Da Fies; Daniel Peck; Martin Dutko; Gennady Mishuris

doi:10.1177/10812865221117553

A temporal averaging–based approach to toughness homogenisation in heterogeneous material

Gaspare Da Fies, Daniel Peck, Martin Dutko, Gennady Mishuris^*

^*Corresponding author for this work

Department of Mathematics

Rockfield

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

A new approach to defining the effective fracture toughness for heterogeneous materials is proposed. This temporal averaging approach is process dependent, incorporating the crack velocity and material toughness. The effectiveness of the new technique is investigated in the context of hydraulic fracture through heterogeneous rock with a periodic material toughness. The plane strain model is considered without fluid leak-off, to more easily investigate different regimes (toughness/viscosity). Numerical simulations are used to examine the effectiveness of the new homogenisation strategy, with comparison against the recently proposed maximum toughness strategy. Simulations are conducted using an extremely effective (in house-built) time–space adaptive solver. The regimes in which each strategy is effective are determined.

Original language	English
Journal	Mathematics and Mechanics of Solids
DOIs	https://doi.org/10.1177/10812865221117553
Publication status	Published - 21 Sept 2022

Keywords

Hydraulic fracture
impermeable rock
periodic toughness distribution
toughness averaging
various regimes

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10.1177/10812865221117553Licence: CC BY-NC

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title = "A temporal averaging–based approach to toughness homogenisation in heterogeneous material",

abstract = "A new approach to defining the effective fracture toughness for heterogeneous materials is proposed. This temporal averaging approach is process dependent, incorporating the crack velocity and material toughness. The effectiveness of the new technique is investigated in the context of hydraulic fracture through heterogeneous rock with a periodic material toughness. The plane strain model is considered without fluid leak-off, to more easily investigate different regimes (toughness/viscosity). Numerical simulations are used to examine the effectiveness of the new homogenisation strategy, with comparison against the recently proposed maximum toughness strategy. Simulations are conducted using an extremely effective (in house-built) time–space adaptive solver. The regimes in which each strategy is effective are determined.",

keywords = "Hydraulic fracture, impermeable rock, periodic toughness distribution, toughness averaging, various regimes",

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note = "Funding Information: The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors have been funded by Welsh Government via S{\^e}r Cymru Future Generations Industrial Fellowship grant AU224 and the European Union{\textquoteright}s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement EffectFact No. 101008140. Funding Information: G.M. is thankful to the Royal Society for the Wolfson Research Merit Award, while M.D. acknowledges the Royal Academy of Engineering for the Industrial Fellowship. The authors are very grateful to the (anonymous) reviewers for their helpful comments. Publisher Copyright: {\textcopyright} The Author(s) 2022.",

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language = "English",

journal = "Mathematics and Mechanics of Solids",

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AU - Peck, Daniel

AU - Dutko, Martin

AU - Mishuris, Gennady

N1 - Funding Information: The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors have been funded by Welsh Government via Sêr Cymru Future Generations Industrial Fellowship grant AU224 and the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement EffectFact No. 101008140. Funding Information: G.M. is thankful to the Royal Society for the Wolfson Research Merit Award, while M.D. acknowledges the Royal Academy of Engineering for the Industrial Fellowship. The authors are very grateful to the (anonymous) reviewers for their helpful comments. Publisher Copyright: © The Author(s) 2022.

PY - 2022/9/21

Y1 - 2022/9/21

N2 - A new approach to defining the effective fracture toughness for heterogeneous materials is proposed. This temporal averaging approach is process dependent, incorporating the crack velocity and material toughness. The effectiveness of the new technique is investigated in the context of hydraulic fracture through heterogeneous rock with a periodic material toughness. The plane strain model is considered without fluid leak-off, to more easily investigate different regimes (toughness/viscosity). Numerical simulations are used to examine the effectiveness of the new homogenisation strategy, with comparison against the recently proposed maximum toughness strategy. Simulations are conducted using an extremely effective (in house-built) time–space adaptive solver. The regimes in which each strategy is effective are determined.

AB - A new approach to defining the effective fracture toughness for heterogeneous materials is proposed. This temporal averaging approach is process dependent, incorporating the crack velocity and material toughness. The effectiveness of the new technique is investigated in the context of hydraulic fracture through heterogeneous rock with a periodic material toughness. The plane strain model is considered without fluid leak-off, to more easily investigate different regimes (toughness/viscosity). Numerical simulations are used to examine the effectiveness of the new homogenisation strategy, with comparison against the recently proposed maximum toughness strategy. Simulations are conducted using an extremely effective (in house-built) time–space adaptive solver. The regimes in which each strategy is effective are determined.

KW - Hydraulic fracture

KW - impermeable rock

KW - periodic toughness distribution

KW - toughness averaging

KW - various regimes

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JO - Mathematics and Mechanics of Solids

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ER -

A temporal averaging–based approach to toughness homogenisation in heterogeneous material

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New Findings Reported from Aberystwyth University Describe Advances in Mathematics and Mechanics of Solids (A Temporal Averaging-based Approach To Toughness Homogenisation In Heterogeneous Material)

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A temporal averaging–based approach to toughness homogenisation in heterogeneous material

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New Findings Reported from Aberystwyth University Describe Advances in Mathematics and Mechanics of Solids (A Temporal Averaging-based Approach To Toughness Homogenisation In Heterogeneous Material)

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