A new finite element code for the study of strain-localization under strike-slip faults

Shear localization under strike-slip faults in ductile conditions remains a matter of debate. The rheology of rocks in the ductile regime is fundamentally strain-rate hardening, which complicates the understanding of the formation of narrow shear zones. Localized shear zones are present in a variety of scales, including kilometric structures at plate boundaries. To compensate for strain-rate hardening, shear zones must be weaker than their surroundings thanks to some weakening mechanism that works at multiple length scales. Mechanisms as shear heating or grain size reduction have been invoked to explain localization of deformation, but none of these mechanisms can work in scales that range from 1 to 1000 km. Layered fabric development has been suggested as a candidate to develop localized shear zones at multiple scales. To test this hypothesis, we have developed a new software that uses the Finite Element Method library deal.II written in C++. We solve the elasticity equations for elastic and Maxwell visco-elastic mediums. A key component required to study strain localization is adaptive mesh refinement. The code automatically identifies those regions in which the deformation is being localized and will increase the resolution. We benchmark the code and test its accuracy using analytical solutions of strike-slip deformation with different boundary conditions. We simulate the instantaneous deformation caused by two kinds of dislocations: a free fault subject to a far field traction and fault with an imposed displacement. We also simulate the visco-elastic relaxation following a strike-slip dislocation. We show that deal.II is a flexible library, suitable for different problems, which will prove useful to study the mechanisms that can lead to strain localization.