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In this article, we describe the mathematical formulation and the numericalimplementation of an effective parametrization of the viscous anisotropy oforthorhombic materials produced by crystallographic preferred orientations (CPOor texture), which can be integrated into 3D geodynamic and materials sciencecodes. Here, the approach is applied to characterize the texture-inducedviscous anisotropy of olivine polycrystals, the main constituent of the Earth'supper mantle. The parameterization is based on the Hill (1948) orthotropicyield criterion. The coefficients of the Hill yield surface are calibratedbased on numerical tests performed using the second order ViscoplasticSelf-consistent (SO-VPSC) model. The parametrization was implemented in a 3Dthermo-mechanical finite-element code developed to model large-scalegeodynamical flows, in the form of a Maxwell rheology combining isotropicelastic and anisotropic non-linear viscous behaviors. The implementation wasvalidated by comparison with results of the analytical solution and of theSO-VPSC model for simple shear and axial compression of a homogeneousanisotropic material. An application designed to examine the effect oftexture-induced viscous anisotropy on the reactivation of mantle shear zones incontinental plates highlights unexpected couplings between localizeddeformation controlled by variations in the orientation and intensity of theolivine texture in the mantle and the mechanical behavior of theelasto-viscoplastic overlying crust. Importantly, the computational time onlyincreases by a factor 2-3 with respect to the classic isotropic Maxwellviscoelastic rheology.

An effective parameterization of texture-induced viscous anisotropy in orthotropic materials with application for modeling geodynamical flows