GPU-based numerical models of rapid ductile strain localization due to thermal runaway

Strain localization is a crucial process for lithosphere and mantle deformation as it allows for the formation of faults and shear zones that enable plate tectonics. In the crust, strain localization usually occurs via brittle failure (i.e., breaking the rock). The deeper and/or hotter the setting, the less likely brittle failure becomes as the critical stress increases with the increasing overburden pressure while the temperature-dependent rheology of rocks limits the stresses that can be accumulated before being relaxed by slow, viscous flow.

Yet, we do observe fast and localized deformation (i.e., earthquakes) at depths of several hundred kilometers. These deep earthquakes either require local differential stresses of several Gigapascal (GPa) to trigger brittle failure or a different, ductile failure mechanism that significantly reduces rock strength while at the same time creating highly localized shear zones. Here, we investigate the feedback loop of visco-elastic deformation and shear heating to determine whether their combination can lead to a localized viscosity reduction and allow for fast slip.

Modeling this feedback loop and the accompanying strong localization of deformation poses a challenge for continuum modeling approaches, in particular when highly nonlinear rheologies such as dislocation creep and low-temperature plasticity are employed. Here, we present a collection of 1D and 2D numerical codes written in the Julia language which use the pseudo-transient approach and graphical processing unit (GPU) computing to model the process of ductile localization and thermal runaway in a simple-shear setting. Our models employ a nonlinear, visco-elastic rheology, including grain-size-dependent diffusion creep, stress-dependent dislocation creep and low-temperature plasticity. We find that the combination of the aforementioned mechanisms is sufficient for deformation to localize on a small perturbation and then propagate through the model similar to a brittle rupture. Our models show that low-temperature plasticity acts as a stress-limiting mechanism that facilitates numerical stability during thermal runaway. In a systematic series of models, we investigate under which conditions thermal runaway occurs and which role each of the rheological components plays in the localization process.