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dc.contributor.authorGabriel, Alice-Agnes
dc.contributor.authorLi, D.
dc.contributor.authorChiocchetti, S.
dc.contributor.authorTavelli, M.
dc.contributor.authorPeshkov, I.
dc.contributor.authorRomenski, E.
dc.contributor.authorDumbser, M.
dc.date.accessioned2020-07-22T13:36:18Z
dc.date.available2020-07-22T13:36:18Z
dc.date.issued2021-03-15
dc.identifier.citationGabriel, A.-A., Li, D., Chiocchetti, S., Tavelli, M., Peshkov, I., Romenski, E., & Dumbser, M. (2021). A unified first-order hyperbolic model for nonlinear dynamic rupture processes in diffuse fracture zones. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 379(2196), 20200130. doi:10.1098/rsta.2020.0130
dc.identifier.issn1364-503X
dc.identifier.issn1471-2962
dc.identifier.doi10.1098/rsta.2020.0130
dc.identifier.urihttp://hdl.handle.net/10754/664359
dc.description.abstractEarthquake fault zones are more complex, both geometrically and rheologically, than an idealized infinitely thin plane embedded in linear elastic material. To incorporate nonlinear material behaviour, natural complexities and multi-physics coupling within and outside of fault zones, here we present a first-order hyperbolic and thermodynamically compatible mathematical model for a continuum in a gravitational field which provides a unified description of nonlinear elasto-plasticity, material damage and of viscous Newtonian flows with phase transition between solid and liquid phases. The fault geometry and secondary cracks are described via a scalar function ξ ∈ [0, 1] that indicates the local level of material damage. The model also permits the representation of arbitrarily complex geometries via a diffuse interface approach based on the solid volume fraction function α ∈ [0, 1]. Neither of the two scalar fields ξ and α needs to be mesh-aligned, allowing thus faults and cracks with complex topology and the use of adaptive Cartesian meshes (AMR). The model shares common features with phase-field approaches, but substantially extends them. We show a wide range of numerical applications that are relevant for dynamic earthquake rupture in fault zones, including the co-seismic generation of secondary off-fault shear cracks, tensile rock fracture in the Brazilian disc test, as well as a natural convection problem in molten rock-like material. This article is part of the theme issue ‘Fracture dynamics of solid materials: from particles to the globe’.
dc.description.sponsorshipThis research has been supported by the European Union’s Horizon 2020 Research and Innovation Programme under the projects ExaHyPE, grant no. 671698, ChEESE, grant no. 823844 and TEAR, grant no. 852992. M.D. and I.P. also acknowledge funding from the Italian Ministry of Education, University and Research (MIUR) via the Departments of Excellence Initiative 2018–2022 attributed to DICAM of the University of Trento (grant L. 232/2016) and the PRIN 2017 project Innovative numerical methods for evolutionary partial differential equations and applications. SC was also funded by the Deutsche Forschungsgemeinschaft (DFG) under the project DROPIT, grant no. GRK 2160/1. E.R. was also funded within the framework of the state contract of the Sobolev Institute of Mathematics (project no. 0314-2019-0012). A.G. also acknowledges funding by the German Research Foundation (DFG) (grants nos GA 2465/2-1, GA 2465/3-1), by KAUSTCRG (grant nos ORS-2017-CRG6 3389.02) and by KONWIHR (project NewWave). Computing resources were provided by th
dc.publisherThe Royal Society
dc.relation.urlhttps://royalsocietypublishing.org/doi/10.1098/rsta.2020.0130
dc.rightsArchived with thanks to Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
dc.titleA unified first-order hyperbolic model for nonlinear dynamic rupture processes in diffuse fracture zones
dc.typeArticle
dc.identifier.journalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
dc.eprint.versionPost-print
dc.contributor.institutionLudwig-Maximilians-Universität München, Theresienstr. 41, 80333 München, Germany
dc.contributor.institutionLaboratory of Applied Mathematics, University of Trento, Via Mesiano, 77, 38123 Trento, Italy
dc.contributor.institutionSobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, 630090 Novosibirsk, Russia
dc.identifier.volume379
dc.identifier.issue2196
dc.identifier.pages20200130
dc.identifier.arxivid2007.01026
kaust.grant.numberORS-2017-CRG6 3389.02
dc.date.accepted2020-09-28
refterms.dateFOA2020-07-22T13:37:13Z
kaust.acknowledged.supportUnitCRG
dc.date.published-online2021-03-15
dc.date.published-print2021-05-03
dc.date.posted2020-07-02


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