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

Gabriel, Alice-Agnes, Duo Li, Simone Chiocchetti, Maurizio Tavelli, Ilya Peshkov, Romenski Evgeniy, and Michael Dumbser (2021), A unified first order hyperbolic model for nonlinear dynamic rupture processes in diffuse fracture zones, Philosophical Transactions of the Royal Society A, 379(2196), doi:10.1098/rsta.2020.0130.

Abstract
Earthquake fault zones are more complex, both geometrically and rheologically, than an idealised 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.
Further information
BibTeX
@article{id2608,
  author = {Alice-Agnes Gabriel and Duo Li and Simone  Chiocchetti and Maurizio Tavelli and Ilya  Peshkov and Romenski Evgeniy and Michael Dumbser},
  journal = {Philosophical Transactions of the Royal Society A},
  number = {2196},
  title = {{A unified first order hyperbolic model for nonlinear dynamic rupture processes in diffuse fracture zones}},
  volume = {379},
  year = {2021},
  url = {https://royalsocietypublishing.org/doi/full/10.1098/rsta.2020.0130},
  doi = {10.1098/rsta.2020.0130},
}
EndNote
%0 Journal Article
%A Gabriel, Alice-Agnes 
%A Li, Duo
%A Chiocchetti, Simone 
%A Tavelli, Maurizio
%A Peshkov, Ilya 
%A Evgeniy, Romenski
%A Dumbser, Michael
%D 2021
%N 2196
%V 379
%J Philosophical Transactions of the Royal Society A
%T A unified first order hyperbolic model for nonlinear dynamic rupture processes in diffuse fracture zones
%U https://royalsocietypublishing.org/doi/full/10.1098/rsta.2020.0130
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Printed 02. Dec 2021 10:14