Modeling lithospheric deformation using a compressible visco‐elasto‐viscoplastic rheology and the effective viscosity approach

Deformations of the colder regions of the lithosphere mainly occur in the frictional regime. In geodynamic models, frictional plastic deformations are often highly localized (shear bands) and are used as proxies for faults. However, capturing the generation and evolution of shear bands in geodynamic models is troublesome. Indeed, mesh dependency and lack of convergence affect, to some extent, the results of geodynamic models. Here we extend the most common plasticity implementation used in geodynamic codes (effective viscosity approach [EVA]) to include the combined effects of elastic compressibility, plastic dilatancy, strain softening, and viscoplasticity. The latter acts as a regularization that cures most of the known issues of geodynamic models related to frictional plasticity. Using regularized models based on the M2Di MATLAB routines, we show that volumetric elasto-plastic deformations can significantly impact crustal-scale shear banding. We also show that the artificial overstress caused by viscoplasticity can be mitigated by employing power-law models. Furthermore, we demonstrate that plasticity algorithms common in geodynamics (based on the EVA) can be as accurate as those obtained with algorithms typically used in engineering (return mapping with a consistent tangent operator). Finally, we show examples of long-term tectonic deformations using the state-of-the art geodynamic code MDoodz. They indicate that viscoplastic regularization can be used efficiently to obtain reliable simulations in geodynamics.