@inbook{5309d36253a14244a37235995b76839a,
title = "Averaging-Based Approach to Toughness Homogenisation for Radial Hydraulic Fracture",
abstract = "The homogenisation of the fracture toughness is considered in the context of a propagating hydraulic fracture. The radial (penny-shape) model is utilised, in order to incorporate the impact of the viscosity-toughness regime transition over time. A homogenisation strategy based on temporal averaging is investigated. This approach incorporates the instantaneous fracture velocity, meaning that it should remain effective in the case of step-wise crack advancement. The effectiveness of the approach is demonstrated for periodic toughness distributions, including those which are unbalanced, utilising a highly accurate solver.",
author = "{Da fies}, G. and M. Dutko and D. Peck",
note = "Funding Information: Acknowledgements MD acknowledges the Royal Academy of Engineering for the Industrial Fellowship. The authors would like to thank Prof. Gennady Mishuris for his continuous interest and helpful discussions during the course of this work. Funding Information: The dependence on the instantaneous velocity does however lead to the most significant open question regarding the proposed strategy. For this work, the results of existing numerical simulations were used to provide the instantaneous velocity used to compute the average toughness. In HF, however, such data is not typically available in real time. Developing an effective approach to computing (or approximating) measures (5.16)–(5.19) in the general case remains an open problem. Funding The authors have been funded by the European Union{\textquoteright}s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement Effect Fact No 101008140 and the Welsh Government via S{\^e}r Cymru Future Generations Industrial Fellowship grant AU224. Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.",
year = "2023",
month = jul,
day = "13",
doi = "10.1007/978-3-031-28744-2_5",
language = "English",
isbn = "9783031287435",
series = "Advanced Structured Materials",
publisher = "Springer Nature",
pages = "69--103",
editor = "Holm Altenbach and Giovanni Bruno and Eremeyev, {Victor A.} and Gutkin, {Mikhail Yu.} and M{\"u}ller, {Wolfgang H.}",
booktitle = "Mechanics of Heterogeneous Materials",
address = "Switzerland",
edition = "1",
}