Articles | Volume 19, issue 1
https://doi.org/10.5194/gmd-19-369-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Special issue:
https://doi.org/10.5194/gmd-19-369-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Development and technical paper
| 
14 Jan 2026
Development and technical paper |
| 14 Jan 2026
| 14 Jan 2026
Overcoming the numerical challenges owing to rapid ductile localization with DEDLoc (version 1.0.0)
Bayerisches Geoinstitut, Universität Bayreuth, Universitätsstraße 30, 95447 Bayreuth, Germany
Marcel Thielmann
CORRESPONDING AUTHOR
Bayerisches Geoinstitut, Universität Bayreuth, Universitätsstraße 30, 95447 Bayreuth, Germany
Institut für Geowissenschaften, Universität Bonn, Meckenheimer Allee 176, 53115 Bonn, Germany
Casper Pranger
Department für Geo- und Umweltwissenschaften, Ludwig-Maximilians-Universität München, Theresienstraße 41, 80333 München, Germany
Albert de Montserrat
Department of Earth Sciences, ETH Zürich, Sonneggstrasse 5, 8092 Zürich, Switzerland
Ludovic Räss
Swiss Geocomputing Centre, Faculty of Geosciences and Environment, University of Lausanne, Lausanne, Switzerland
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Cited articles
Alkhimenkov, Y. and Podladchikov, Y. Y.: Accelerated pseudo-transient method for elastic, viscoelastic, and coupled hydromechanical problems with applications, Geosci. Model Dev., 18, 563–583, https://doi.org/10.5194/gmd-18-563-2025, 2025. a, b
Alkhimenkov, Y., Khakimova, L., Utkin, I., and Podladchikov, Y.: Resolving strain localization in frictional and time-dependent plasticity: Two-and three-dimensional numerical modeling study using graphical processing units (GPUs), J. Geophys. Res.-Sol. Ea., 129, e2023JB028566, https://doi.org/10.1029/2023JB028566, 2024. a
Andersen, T. B., Austrheim, H., Deseta, N., Silkoset, P., and Ashwal, L. D.: Large subduction earthquakes along the fossil Moho in Alpine Corsica, Geology, 42, 395–398, 2014. a
Antolovich, S. D. and Armstrong, R. W.: Plastic strain localization in metals: origins and consequences, Progress in Materials Science, 59, 1–160, https://doi.org/10.1016/j.pmatsci.2013.06.001, 2014. a
Auzemery, A., Willingshofer, E., Yamato, P., Duretz, T., and Sokoutis, D.: Strain localization mechanisms for subduction initiation at passive margins, Global Planet. Change, 195, 103323, https://doi.org/10.1016/j.gloplacha.2020.103323, 2020. a
Barras, F. and Brantut, N.: Shear localisation controls the dynamics of earthquakes, Nat. Commun., 16, 711, https://doi.org/10.1038/s41467-024-55363-y, 2025. a
Braeck, S., Podladchikov, Y. Y., and Medvedev, S.: Spontaneous dissipation of elastic energy by self-localizing thermal runaway, Phys. Rev. E, 80, 046105, https://doi.org/10.1103/PhysRevE.80.046105, 2009. a, b
Brantut, N., Stefanou, I., and Sulem, J.: Dehydration-induced instabilities at intermediate depths in subduction zones, J. Geophys. Res.-Sol. Ea., 122, 6087–6107, 2017. a
Burg, J.-P.: Ductile structures and instabilities: their implication for Variscan tectonics in the Ardennes, Tectonophysics, 309, 1–25, 1999. a
Bursi, O. S. and Shing, P.-S.: Evaluation of some implicit time-stepping algorithms for pseudodynamic tests, Earthq. Eng. Struct. D, 25, 333–355, 1996. a
Byerlee, J.: Friction of rocks, in: Rock friction and earthquake prediction, Birkhäuser, Basel, 615–626, https://doi.org/10.1007/978-3-0348-7182-2, 1978. a
Cross, A. and Skemer, P.: Rates of dynamic recrystallization in geologic materials, J. Geophys. Res.-Sol. Ea., 124, 1324–1342, 2019. a
Dal Zilio, L., Hegyi, B., Behr, W., and Gerya, T.: Hydro-mechanical earthquake cycles in a poro-visco-elasto-plastic fluid-bearing fault structure, Tectonophysics, 838, 229516, https://doi.org/10.1016/j.tecto.2022.229516, 2022. a
Darve, F. and Laouafa, F.: Instabilities in granular materials and application to landslides, Mechanics of Cohesive-frictional Materials: An International Journal on Experiments, Modelling and Computation of Materials and Structures, 5, 627–652, 2000. a
De Borst, R. and Mühlhaus, H.-B.: Gradient-dependent plasticity: formulation and algorithmic aspects, Int. J. Numer. Meth. Eng., 35, 521–539, https://doi.org/10.1002/nme.1620350307, 1992. a
De Borst, R., Sluys, L. J., Muhlhaus, H.-B., and Pamin, J.: Fundamental issues in finite element analyses of localization of deformation, Engineering Computations, 10, 99–121, https://doi.org/10.1108/eb023897, 1993. a, b, c
Desrues, J., Bésuelle, P., and Lewis, H.: Strain localization in geomaterials, Geological Society, London, Special Publications, 289, 47–73, https://doi.org/10.1144/SP289.4, 2007. a
Drucker, D. C. and Prager, W.: Soil mechanics and plastic analysis or limit design, Quarterly of Applied Mathematics, 10, 157–165, 1952. a
Duretz, T., Räss, L., Podladchikov, Y., and Schmalholz, S.: Resolving thermomechanical coupling in two and three dimensions: spontaneous strain localization owing to shear heating, Geophys. J. Int., 216, 365–379, https://doi.org/10.1093/gji/ggy434, 2019. a, b
Duretz, T., de Borst, R., Yamato, P., and Le Pourhiet, L.: Toward robust and predictive geodynamic modeling: The way forward in frictional plasticity, Geophys. Res. Lett., 47, e2019GL086027, https://doi.org/10.1029/2019GL086027, 2020. a, b
Duretz, T., Räss, L., de Borst, R., and Hageman, T.: A comparison of plasticity regularization approaches for geodynamic modeling, Geochem. Geophy. Geosy., 24, e2022GC010675, https://doi.org/10.1029/2022GC010675, 2023. a, b
Gerolymatou, E., Stathas, A., and Stefanou, I.: Do multiphysics processes lead to mesh independent analyses?, International Journal of Mechanical Sciences, 274, 109265, https://doi.org/10.1016/j.ijmecsci.2024.109265, 2024. a, b, c
Gerya, T. V.: Introduction to numerical geodynamic modelling, Cambridge University Press, https://doi.org/10.1017/9781316534243, 2019. a, b
Gerya, T. V. and Yuen, D. A.: Characteristics-based marker-in-cell method with conservative finite-differences schemes for modeling geological flows with strongly variable transport properties, Phys. Earth Planet. In., 140, 293–318, https://doi.org/10.1016/j.pepi.2003.09.006, 2003. a
Gleason, G. C. and Green II, H. W.: A general test of the hypothesis that transformation-induced faulting cannot occur in the lower mantle, Phys. Earth Planet. In., 172, 91–103, 2009. a
Goudarzi, M., Gerya, T., and Dinther, Y. v.: A comparative analysis of continuum plasticity, viscoplasticity and phase-field models for earthquake sequence modeling, Comput. Mech., 72, 615–633, https://doi.org/10.1007/s00466-023-02311-0, 2023. a, b
Gruntfest, I.: Thermal feedback in liquid flow; plane shear at constant stress, Transactions of the Society of Rheology, 7, 195–207, https://doi.org/10.1122/1.548954, 1963. a
Hacker, B. R., Peacock, S. M., Abers, G. A., and Holloway, S. D.: Subduction factory 2. Are intermediate-depth earthquakes in subducting slabs linked to metamorphic dehydration reactions?, J. Geophys. Res.-Sol. Ea., 108, https://doi.org/10.1029/2001JB001129, 2003. a
Hansen, L. N., Kumamoto, K. M., Thom, C. A., Wallis, D., Durham, W. B., Goldsby, D. L., Breithaupt, T., Meyers, C. D., and Kohlstedt, D. L.: Low-temperature plasticity in olivine: Grain size, strain hardening, and the strength of the lithosphere, J. Geophys. Res.-Sol. Ea., 124, 5427–5449, https://doi.org/10.1029/2018JB016736, 2019. a, b
Herrendörfer, R., Gerya, T., and van Dinther, Y.: An invariant rate-and state-dependent friction formulation for viscoeastoplastic earthquake cycle simulations, J. Geophys. Res.-Sol. Ea., 123, 5018–5051, https://doi.org/10.1029/2017JB015225, 2018. a
Iordache, M.-M. and Willam, K.: Localized failure analysis in elastoplastic Cosserat continua, Computer Methods in Applied Mechanics and Engineering, 151, 559–586, https://doi.org/10.1016/S0045-7825(97)00166-7, 1998. a, b
Jacquey, A. B. and Cacace, M.: Multiphysics modeling of a brittle-ductile lithosphere: 1. Explicit visco-elasto-plastic formulation and its numerical implementation, J. Geophys. Res.-Sol. Ea., 125, e2019JB018474, https://doi.org/10.1029/2019JB018474, 2020. a
Jacquey, A. B., Rattez, H., and Veveakis, M.: Strain localization regularization and patterns formation in rate-dependent plastic materials with multiphysics coupling, J. Mech. Phys. Solids, 152, 104422, https://doi.org/10.1016/j.jmps.2021.104422, 2021. a
Jóźwiak, B., Orczykowska, M., and Dziubiński, M.: Fractional generalizations of Maxwell and Kelvin-Voigt models for biopolymer characterization, PloS One, 10, e0143090, https://doi.org/10.1371/journal.pone.0143090, 2015. a, b
Kameyama, M., Yuen, D. A., and Karato, S.-I.: Thermal-mechanical effects of low-temperature plasticity (the Peierls mechanism) on the deformation of a viscoelastic shear zone, Earth Planet. Sc. Lett., 168, 159–172, https://doi.org/10.1016/S0012-821X(99)00040-0, 1999. a, b
Katz, R. F., Spiegelman, M., and Langmuir, C. H.: A new parameterization of hydrous mantle melting, Geochem. Geophy. Geosy., 4, https://doi.org/10.1029/2002GC000433, 2003. a
Katz, R. F., Spiegelman, M., and Holtzman, B.: The dynamics of melt and shear localization in partially molten aggregates, Nature, 442, 676–679, 2006. a
Kaus, B. J. P., de Montserrat, A., Medinger, N., Riel, N., Cosarinky, M., Berlie, N., Spang, A., Kiss, D., Ranocha, H., Fuchs, L., Räss, L., Aellig, P., Seiler, A., and Duretz, T.: JuliaGeodynamics/GeoParams.jl: v0.5.1, Zenodo [code], https://doi.org/10.5281/zenodo.10050339, 2023. a
Kelemen, P. B. and Hirth, G.: A periodic shear-heating mechanism for intermediate-depth earthquakes in the mantle, Nature, 446, 787–790, https://doi.org/10.1038/nature05717, 2007. a
Kirby, S. H., Stein, S., Okal, E. A., and Rubie, D. C.: Metastable mantle phase transformations and deep earthquakes in subducting oceanic lithosphere, Rev. Geophys., 34, 261–306, 1996. a
Kiss, D., Moulas, E., Kaus, B. J. P., and Spang, A.: Decompression and fracturing caused by magmatically induced thermal stresses, J. Geophys. Res.-Sol. Ea., 128, e2022JB025341, https://doi.org/10.1029/2022JB025341, 2023. a
Leith, A. and Sharpe, J.: Deep-focus earthquakes and their geological significance, J. Geol., 44, 877–917, https://doi.org/10.1086/624495, 1936. a
Liebske, C., Schmickler, B., Terasaki, H., Poe, B. T., Suzuki, A., Funakoshi, K.-I., Ando, R., and Rubie, D. C.: Viscosity of peridotite liquid up to 13 GPa: Implications for magma ocean viscosities, Earth Planet. Sc. Lett., 240, 589–604, 2005. a
Maxwell, J. C.: IV. On the dynamical theory of gases, Philosophical Transactions of the Royal Society of London, 49–88, https://doi.org/10.1098/rstl.1867.0004, 1867. a, b
Mulyukova, E. and Bercovici, D.: Formation of lithospheric shear zones: Effect of temperature on two-phase grain damage, Phys. Earth Planet. In., 270, 195–212, 2017. a
Ogawa, M.: Shear instability in a viscoelastic material as the cause of deep focus earthquakes, J. Geophys. Res.-Sol. Ea., 92, 13801–13810, https://doi.org/10.1029/JB092iB13p13801, 1987. a, b, c
Omlin, S. and Räss, L.: High-performance xPU Stencil Computations in Julia, Proceedings of the JuliaCon Conferences, 6, 138, https://doi.org/10.21105/jcon.00138, 2024. a
Omlin, S., Räss, L., Aloisi, G., de Montserrat, A., Aellig, P., Ranocha, H., Schnetter, E., and Churavy, V.: omlins/ParallelStencil.jl: ParallelStencil.jl 0.14.3 (v0.14.3), Zenodo [code], https://doi.org/10.5281/zenodo.15921651, 2025. a
Poirier, J.: Shear localization and shear instability in materials in the ductile field, J. Struct. Geol., 2, 135–142, https://doi.org/10.1016/0191-8141(80)90043-7, 1980. a, b
Pranger, C., Sanan, P., May, D. A., Le Pourhiet, L., and Gabriel, A.-A.: Rate and state friction as a spatially regularized transient viscous flow law, J. Geophys. Res.-Sol. Ea., 127, e2021JB023511, https://doi.org/10.1029/2021JB023511, 2022. a, b, c
Räss, L., Utkin, I., Duretz, T., Omlin, S., and Podladchikov, Y. Y.: Assessing the robustness and scalability of the accelerated pseudo-transient method, Geosci. Model Dev., 15, 5757–5786, https://doi.org/10.5194/gmd-15-5757-2022, 2022. a, b, c
Ropp, D. L., Shadid, J. N., and Ober, C. C.: Studies of the accuracy of time integration methods for reaction–diffusion equations, Journal of Computational Physics, 194, 544–574, https://doi.org/10.1016/j.jcp.2003.08.033, 2004. a
Rowe, C. D., Kirkpatrick, J. D., and Brodsky, E. E.: Fault rock injections record paleo-earthquakes, Earth Planet. Sc. Lett., 335, 154–166, 2012. a
Roy, S., Koons, P., Upton, P., and Tucker, G.: Dynamic links among rock damage, erosion, and strain during orogenesis, Geology, 44, 583–586, 2016. a
Ruh, J., Behr, W., and Tokle, L.: Effect of grain-size and textural weakening in polyphase crustal and mantle lithospheric shear zones, Tektonika, 2, 91–110, 2024. a
Rylander, T. and Bondeson, A.: Stability of explicit–implicit hybrid time-stepping schemes for Maxwell's equations, Journal of Computational Physics, 179, 426–438, 2002. a
Sleep, N. H.: Application of a unified rate and state friction theory to the mechanics of fault zones with strain localization, J. Geophys. Res.-Sol. Ea., 102, 2875–2895, https://doi.org/10.1029/96JB03410, 1997. a
Söderlind, G. and Wang, L.: Adaptive time-stepping and computational stability, Journal of Computational and Applied Mathematics, 185, 225–243, 2006. a
Spang, A., Thielmann, M., Pranger, C., de Montserrat, A., and Räss, L. G.: Numerical model used in “Overcoming the numerical challenges owing to rapid ductile localization”, Zenodo [code, video supplement], https://doi.org/10.5281/zenodo.17592601, 2025b. a, b
Spiegelman, M., May, D. A., and Wilson, C. R.: On the solvability of incompressible Stokes with viscoplastic rheologies in geodynamics, Geochem. Geophy. Geosy., 17, 2213–2238, 2016. a
Thielmann, M.: Grain size assisted thermal runaway as a nucleation mechanism for continental mantle earthquakes: Impact of complex rheologies, Tectonophysics, 746, 611–623, https://doi.org/10.1016/j.tecto.2017.08.038, 2018. a
Thielmann, M., Rozel, A., Kaus, B. J. P., and Ricard, Y.: Intermediate-depth earthquake generation and shear zone formation caused by grain size reduction and shear heating, Geology, 43, 791–794, https://doi.org/10.1130/G36864.1, 2015. a, b, c
Turner, H.: On the Arrival of Earthquake Waves at the Antipodes, and on the Measurement of the Focal Depth of an Earthquake., Geophys. J. Int., 1, 1–13, https://doi.org/10.1111/j.1365-246X.1922.tb05354.x, 1922. a
Wadati, K.: Shallow and deep earthquakes, Geophys. Mag., 1, 162–202, 1928. a
Weidner, A. and Biermann, H.: Review on strain localization phenomena studied by high-resolution digital image correlation, Advanced Engineering Materials, 23, 2001409, https://doi.org/10.1002/adem.202001409, 2021. a
Xie, L., Yoneda, A., Katsura, T., Andrault, D., Tange, Y., and Higo, Y.: Direct viscosity measurement of peridotite melt to lower-mantle conditions: a further support for a fractional magma-ocean solidification at the top of the lower mantle, Geophys. Res. Lett., 48, e2021GL094507, https://doi.org/10.1029/2021GL094507, 2021. a
Short summary
Concentration of deformation is difficult to capture accurately in computer simulations. We present a number of challenges associated with concentrated viscous deformation and demonstrate strategies to overcome them. The strategies include automatic selection of appropriate time steps to react to rapid changes in model behavior, automatic rescaling to avoid rounding errors, and three methods to prevent model instability. This way, we are able to accurately capture very fast viscous deformation.
Concentration of deformation is difficult to capture accurately in computer simulations. We...
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