A voyage through the deformed Earth with the self-consistent model

The viscoplastic self-consistent (VPSC) large strain polycrystal plasticity theory proved to be very useful for modelling the deformation in Earth materials. In contrast to most metals, rocks are composed of low-symmetry minerals with few slip systems. Also, most minerals have a high strain-rate sensitivity. Consequently, different orientations deform at different rates, contrary to the assumptions of the traditional Taylor model. The self-consistent method has been applied to predict textures and microstructures in many mineral systems and some highlights will be reviewed.

Starting at the surface of the Earth, ice deforms mainly by basal slip. Texture patterns observed in experiments and in the large polar ice sheets are well predicted with the VPSC model. In sediments, concentrations of salt (halite) deform by buoyant upwelling into salt domes. When VPSC was applied to halite, entirely different textures were predicted than those with the Taylor model, in better accordance with low temperature deformation experiments where {110}10 is the prevalent slip system. Calcite has been an excellent example to illustrate how textures measured in natural rocks can be used to infer the deformation history in the Earth's crust. In calcite, VPSC automatically simulates the effects of `curling' in axial compression, producing plane strain deformation at the microscopic scale. Many minerals are recrystallized. VPSC has been used as the basis of a model for dynamic recrystallization which balances nucleation of highly deformed grains and growth of less deformed grains. Applying it to quartz made it possible to explain textures in naturally deformed quartzites, particularly those deformed in simple shear. The upper mantle of the Earth is largely composed of olivine and deforms in large convection cells that extend over thousands of kilometres. Polycrystal plasticity predicts a highly heterogeneous texture evolution along streamlines with strong development of preferred orientation. Since single crystals of olivine are elastically anisotropic, oriented polycrystals also display anisotropy. Predicted anisotropies of seismic wave velocities of 5-10% in the model mantle agree well with those observed by seismologists. Finally the still highly enigmatic inner core is composed of solid -iron (hexagonal close packed) and seismologists have observed that wave velocities are slightly higher parallel to the Earth's axis than in the equatorial plane. Again, VPSC simulations suggest that this anisotropy in the centre of the Earth could be due to deformation during convection.

The examples illustrate, on a grand scale, that VPSC has not only helped us to unravel the deformation history of the Earth but also contributes towards to a better understanding of the deformation behaviour of complex and anisotropic materials.