A unified first-order hyperbolic model for nonlinear dynamic rupture processes in diffuse fracture zones

Alice-Agnes Gabriel, D. Li, S. Chiocchetti, M. Tavelli, I. Peshkov, E. Romenski, M. Dumbser

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


Earthquake 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’.
Original languageEnglish (US)
Pages (from-to)20200130
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2196
StatePublished - Mar 15 2021
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2021-03-23
Acknowledged KAUST grant number(s): ORS-2017-CRG6 3389.02
Acknowledgements: This 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
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Engineering(all)
  • Mathematics(all)


Dive into the research topics of 'A unified first-order hyperbolic model for nonlinear dynamic rupture processes in diffuse fracture zones'. Together they form a unique fingerprint.

Cite this