Resolving thermomechanical coupling in two and three dimensions: Spontaneous strain localization owing to shear heating

Abstract

Numerous geological processes are governed by thermal and mechanical interactions. In particular, tectonic processes such as ductile strain localization can be induced by the intrinsic coupling that exists between deformation, energy and rheology. To investigate this thermomechanical feedback, we have designed 2-D codes that are based on an implicit finite-difference discretization. The direct-iterative method relies on a classical Newton iteration cycle and requires assembly of sparse matrices, while the pseudo-transient method uses pseudo-time integration and is matrix-free. We show that both methods are able to capture thermomechanical instabilities when applied to model thermally activated shear localization; they exhibit similar temporal evolution and deliver coherent results both in terms of nonlinear accuracy and conservativeness. The pseudo-transient method is an attractive alternative, since it can deliver similar accuracy to a standard direct-iterative method but is based on a much simpler algorithm and enables high-resolution simulations in 3-D. We systematically investigate the dimensionless parameters controlling 2-D shear localization and model shear zone propagation in 3-D using the pseudo-transient method. Code examples based on the pseudo-transient and direct-iterative methods are part of the M2Di routines (Räss et al., 2017) and can be downloaded from Bitbucket and the Swiss Geocomputing Centre website.