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 mat erials. Ln contrast to most metals, rocks are composed of low-symmetry mine rals with few slip systems. Also, most minerals have a high strain-rate sen sitivity. Consequently, different orientations deform at different rates, c ontrary to the assumptions of the traditional Taylor model. The self-consis tent method has been applied to predict textures and microstructures in man y mineral systems and some highlights will be reviewed. Starting at the surface of the Earth, ice deforms mainly by basal slip. Tex ture 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 T aylor model, in better accordance with low temperature deformation experime nts where {110}[1 (1) over bar 0] is the prevalent slip system. Calcite has been an excellent example to illustrate how textures measured in natural r ocks can be used to infer the deformation history in the Earth's crust. In calcite, VPSC automatically simulates the effects of 'curling' in axial com pression, producing plane strain deformation at the microscopic scale. Many minerals are recrystallized. VPSC has been used as the basis of a model fo r dynamic recrystallization which balances nucleation of highly deformed gr ains and growth of less deformed grains. Applying it to quartz made it poss ible to explain textures in naturally deformed quartzites, particularly tho se deformed in simple shear. The upper mantle of the Earth is largely compo sed of olivine and deforms in large convection cells that extend over thous ands of kilometres. Polycrystal plasticity predicts a highly heterogeneous texture evolution along streamlines with strong development of preferred or ientation. Since single crystals of olivine are elastically anisotropic, or iented polycrystals also display anisotropy. Predicted anisotropies of seis mic wave velocities of 5-10% in the model mantle agree well with those obse rved by seismologists. Finally the still highly enigmatic inner core is com posed of solid epsilon-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 thi s 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 towar ds to a better understanding of the deformation behaviour of complex and an isotropic materials.