Resolving thermomechanical coupling in two and three dimensions: spontaneous strain localization owing to shear heating
Résumé
Numerous geological processes are governed by thermal and mechanical interactions. In particular,tectonic processes such as ductile strain localization can be induced by the intrinsiccoupling that exists between deformation, energy and rheology. To investigate this thermomechanicalfeedback, we have designed 2-D codes that are based on an implicit finite-differencediscretization. The direct-iterative method relies on a classical Newton iteration cycle andrequires assembly of sparse matrices, while the pseudo-transient method uses pseudo-timeintegration and is matrix-free. We show that both methods are able to capture thermomechanicalinstabilities when applied to model thermally activated shear localization; they exhibitsimilar temporal evolution and deliver coherent results both in terms of nonlinear accuracyand conservativeness. The pseudo-transient method is an attractive alternative, since it candeliver similar accuracy to a standard direct-iterative method but is based on a much simpleralgorithm and enables high-resolution simulations in 3-D. We systematically investigate thedimensionless parameters controlling 2-D shear localization and model shear zone propagationin 3-D using the pseudo-transient method. Code examples based on the pseudo-transientand direct-iterative methods are part of the M2Di routines (R¨ass et al., 2017) and can bedownloaded from Bitbucket and the Swiss Geocomputing Centre website.
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