Modelling lithosphere deformation with non-linear anisotropic constitutive models

The processes that govern rock (trans)formation (deposition, deformation, segregation, metamorphism) can result in the development of layering and rock fabrics. Rocks can thus exhibit extrinsic or intrinsic anisotropy at various spatial scales. Anisotropy has important mechanical consequences, in particular, for strain localisation in the lithosphere. This effect is typically not included in geodynamic models. Mechanical anisotropy can be modelled by explicitly modelled by numerically resolving layers of different strengths. Due to the expensive computational cost, this approach is not suitable for large scale geodynamic models. The latter may rather benefit from an upscaling approach that involves anisotropic constitutive laws.  To model the evolution of such material Mühhlaus, (2002) proposed the use of the director vector which corresponds to a single orientation that is changing throughout the process of deformation. We have implemented visco-elasto-plastic anisotropic constitutive laws and the director vector approach in the geodynamic simulation tool MDoodz7.0. Here we present  the rheological implementation, we show some simple simulations involving anisotropic flow and discuss the potential role of anisotropy for large-scale geodynamic processes.