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

In this article, we describe the mathematical formulation and the numerical implementation of an effective parametrization of the viscous anisotropy of orthorhombic materials produced by crystallographic preferred orientations (CPO or texture), which can be integrated into 3D geodynamic and materials science codes. Here, the approach is applied to characterize the texture-induced viscous anisotropy of olivine polycrystals, the main constituent of the Earth's upper mantle. The parameterization is based on the Hill (1948) orthotropic yield criterion. The coefficients of the Hill yield surface are calibrated based on numerical tests performed using the second order Viscoplastic Self-consistent (SO-VPSC) model. The parametrization was implemented in a 3D thermo-mechanical finite-element code developed to model large-scale geodynamical flows, in the form of a Maxwell rheology combining isotropic elastic and anisotropic non-linear viscous behaviors. The implementation was validated by comparison with results of the analytical solution and of the SO-VPSC model for simple shear and axial compression of a homogeneous anisotropic material. An application designed to examine the effect of texture-induced viscous anisotropy on the reactivation of mantle shear zones in continental plates highlights unexpected couplings between localized deformation controlled by variations in the orientation and intensity of the olivine texture in the mantle and the mechanical behavior of the elasto-viscoplastic overlying crust. Importantly, the computational time only increases by a factor 2-3 with respect to the classic isotropic Maxwell viscoelastic rheology. Comment: 32 pag.; 5 figures; 4 tables

On an elastodynamic classification of orthorhombic media

Sets of elastic constants for crystalline media are normally presented with reference to the axes of the unit cell defined by structural crystallographers (Landolt & Bdrnstein 1979). In orthorhombic materials, the magnitudes of the nine elastic stiffnesses, in general, show little or no consistent correspondence with the suffixes (related to crystal axes) of the physical constants. A classification scheme for orthorhombic media, based on an ordering of the elastodynamically important principal stiffnesses of extension ( c 11 , c 22 , c 33 ) and of shear ( c 44 , c 55 , c 66 ), is described and illustrated. The classification facilitates meaningful comparisons of elastodynamic properties since it offers the following advantages: (i) It is amenable to cyclic interchange. (ii) It permits concise expression of basic homogeneous plane wave theory (Musgrave 1970). (iii) It affords rapid appreciation of the possible essential configurations of homogeneous plane wave slowness in each coordinate plane. (iv) It allows known criteria for the existence of hyperbolic regions in elastic slowness and wave surfaces (Musgrave 1957,1979) and some further developments, to be succinctly expressed. Application of the scheme to the theory of bulk waves is exemplified in detail for three media, diverse in their properties, a-uranium, spruce (wood) and a hypothetical medium discussed by Al’shits & Lothe (19796); specification of exceptional, limiting bulk waves (Chadwick & Smith 1977) is included.