WIAS Preprint No. 2954, (2022)

Qualitative study of a geodynamical rate-and-state model for elastoplastic shear flows in crustal faults


  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888
  • Roubíček, Tomáš
    ORCID: 0000-0002-0651-5959

2020 Mathematics Subject Classification

  • 35Q74 35Q86 74-10 74A55 74C10 74R20 86A15


  • Rate-and-state friction, plasticity, damage, aging, steady states, dynamics, time-discretization, seismic cycles, 1-degree-of-freedom slider




The Dieterich--Ruina rate-and-state friction model is transferred to a bulk variant and the state variable (aging) influencing the dissipation mechanism is here combined also with a damage influencing standardly the elastic response. As the aging has a separate dynamics, the overall model does not have a standard variational structure. A one-dimensional model is investigated as far as the steady-state existence, localization of the cataclastic core, and its time response, too. Computational experiments with a damage-free variant show stick-slip behavior (i.e. seismic cycles of tectonic faults) as well as stable slip under very large velocities.

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