Description: It has been debated for decades whether rigid inclusions, such as porphyroclasts and porphyroblasts, do or do not rotate in a softer matrix during deformation. Experiments and numerical simulations with viscous matrix rheologies show ongoing rotation of circular inclusions, whereas using Mohr-Coulomb plasticity results in nonrotation. Because the rocks in which inclusions are found normally undergo deformation by dislocation creep, we applied a full-field crystal plasticity approach to investigate the rotation behavior of rigid circular inclusions. We show that the inclusion's rotation strongly depends on the anisotropy of the matrix minerals. Strongly anisotropic minerals will develop shear bands that reduce the rotation of inclusions. Inhibition of rotation can only occur after a significant amount of strain. Our results may help to explain why geologic rigid objects often show evidence for rotation, but not necessarily in accordance with the viscous theory that is usually applied to these systems.

Description: Deformation localisation can lead to a variety of structures, such as shear zones and bands that range from grain to crustal scale, from discrete zones to anastomosing networks, and shear zone related folds. We present numerical simulations of the deformation of an intrinsically anisotropic material with a single maximum crystal preferred orientation (CPO) in simple shear. We use the Viscoplastic Full-Field Transform (VPFFT) crystal plasticity code coupled with the modelling platform ELLE to achieve very high strains. The VPFFT-approach simulates deformation by dislocation glide, taking into account the different available slip systems and their critical resolved shear stresses. We vary the anisotropy of the material from isotropic to highly anisotropic, as well as the orientation of the initial CPO. To visualize deformation structures, we use passive markers, for which we also systematically vary the initial orientation. At low strains the amount of strain rate localisation and resulting deformation structures depend on the initial CPO in all anisotropic models. Three regimes can be recognised: distributed shear localisation, synthetic shear bands and antithetic shear bands. However, at very high strains localisation behaviour always tends to converge to a similar state, independent of the initial CPO. Shear localisation is often detected by folded layers, which may be parallel to the anisotropy (e.g. cleavage formed by aligned mica), or the deformation of passive layering, such as original sedimentary layers. The resulting fold patterns vary strongly, depending on the original layer orientation. This can result in misleading structures that seem to indicate the opposite sense of shear.

Description: Deformation localisation can lead to a variety of structures, such as shear zones and shear bands (from grain to crustal scale), from isolated zones to anastomosing networks. The heterogeneous strain field can furthermore result in a wide range of highly diverse fold geometries. In anisotropic materials the deformation behaviour is controlled by the viscoplastic anisotropy of the material and their ability to form a crystallographic preferred orientation (CPO). Here we present a selection of a series of numerical simulations which aim to investigate (1) the influence of an initial CPO in an anisotropic material on localization behaviour and (2) the role of layering/passive markers on the development of deformation structures.

Description: We present a series of simple shear numerical simulations of dynamic recrystallization of two‐phase non‐linear viscous materials that represent temperate ice. Firstly, we investigate the effect of the presence of water on the resulting microstructures and, secondly, how water influences on P‐wave (Vp) and fast S‐wave (Vs) velocities. Regardless the water percentage, all simulations evolve from a random fabric to a vertical single maximum. For a purely solid aggregate, the highest Vp quickly aligns with the maximum c‐axis orientation. At the same time, the maximum c‐axis development reduces Vs in this orientation. When water is present, the developed maximum c‐axis orientation is less intense, which results in lower Vp and Vs. At high percentage of water, Vp does not align with the maximum c‐axis orientation. If the bulk modulus of ice is assumed for the water phase (i.e., implying that water is at high pressure), we find a remarkable decrease of Vs while Vp remains close to the value for purely solid ice. These results suggest that the decrease in Vs observed at the base of the ice sheets could be explained by the presence of water at elevated pressure, which would reside in isolated pockets at grain triple junctions. Under these conditions water would not favor sliding between ice grains. However, if we consider that deformation dominates over recrystallization water pockets get continuously stretched, allowing water films to be located at grain boundaries. This configuration would modify and even overprint the maximum c‐axis‐dependent orientation and the magnitude of seismic anisotropy.

Description: The ice mass balances of Antarctic and Greenland ice sheets represent the largest uncertainty for predicting future sea-level rise. Understanding how ice flows from the accumulation to the ablation zone is therefore crucial for correctly estimating the changing mass in polar ice-sheets. On Earth, ice crystals have a hexagonal symmetry (ice lh) with a strong anisotropy favouring basal slip. This results in a progressive development of a vertical c-axis preferred orientation (LPO) of ice polycrystalline aggregates during deformation. In depth, the elastic anisotropy of polycrystalline ice gradually increases due the development of a vertical LPO. Observations of P-wave (Vp) and S-wave (Vs) velocities in ice sheets reveal a strong decrease of ~25% of Vs in depth, while Vp remains approximately constant. According to Wittlinger and Farra (2015) the low Vs may be due to the presence of unfrozen liquids resulting from pre-melting at grain joints and/or melting of chemical solutions buried in ice. Although previous studies of two-phase rocks (including melt and water) show that seismic velocities depend on both LPO and water content, studies on the effect of melt on polar ice seismic velocity are scarce. In this contribution we investigate the changes in P- and faster S-wave velocities during deformation of polycrystalline ice with different melt fractions.

Description: The flow of glaciers and polar ice sheets is controlled by the highly anisotropic rheology of ice crystals that have hexagonal symmetry (ice lh). To improve our knowledge of ice sheet dynamics, it is necessary to understand how dynamic recrystallization (DRX) controls ice microstructures and rheology at different boundary conditions that range from pure shear flattening at the top to simple shear near the base of the sheets. We present a series of two-dimensional numerical simulations that couple ice deformation with DRX of various intensities, paying special attention to the effect of boundary conditions. The simulations show how similar orientations of c-axis maxima with respect to the finite deformation direction develop regardless of the amount of DRX and applied boundary conditions. In pure shear this direction is parallel to the maximum compressional stress, while it rotates towards the shear direction in simple shear. This leads to strain hardening and increased activity of non-basal slip systems in pure shear and to strain softening in simple shear. Therefore, it is expected that ice is effectively weaker in the lower parts of the ice sheets than in the upper parts. Strain-rate localization occurs in all simulations, especially in simple shear cases. Recrystallization suppresses localization, which necessitates the activation of hard, non-basal slip systems.This article is part of the themed issue {\textquoteleft}Microdynamics of ice{\textquoteright}.

Description: The present study is based on a series of two-dimensional simple shear numerical simulations of two-phase non-linear viscous materials used to investigate the mechanical behaviour of two-phase aggregates representing partially molten rocks. These simulations couple viscoplastic deformation with dynamic recrystallisation (DRX). The aim of these simulations is to investigate the competition between deformation and recrystallisation, and how they affect the mechanical behaviour and resulting microstructures of the deforming material. We systematically vary the melt to solid rock ratio, the dihedral angle of melt and the ratio of DRX vs. deformation. The results show that the amount of DRX and the dihedral angle have a first-order impact on the bulk rheology and the melt distribution in the aggregate. The numerical results allow defining two regimes, depending on the relative contribution of deformation and DRX: (1) a deformation-dominated regime at high strain rates (i.e., with a low ratio of recrystallisation vs. viscoplastic deformation) and (2) a recrystallisation-dominated regime at low strain rates (i.e., with a high ratio of recrystallisation vs. viscoplastic deformation). The first case results in systems bearing large connected melt pockets whose viscous flow controls the deformation of the aggregate, while disconnected smaller melt pockets develop in models where dynamic recrystallisation dominates. The results of this study allow us to better understand the development of connected melt pockets, which may focus melt flow. The distribution of the melt phase plays a key role in the formation of larger-scale melt-enriched shear bands, which in turn has a direct influence on large-scale convective mantle flow.

Description: The occurrence of various types of shear bands (C, C’, C”) in shear zones indicate that heterogeneity of strain is common in strongly deformed rocks. However, the importance of strain localisation is difficult to ascertain if suitable strain markers are lacking, which is usually the case. Numerical modelling with the finite-element method has so far not given much insight in the development of shear bands. We suggest that this is not only because the modelled strains are often not high enough, but also because this technique (that usually assumes isotropic material properties within elements) does not properly incorporate mineral deformation behaviour. We simulated high-strain, simple-shear deformation in single- and polyphase materials with a full-field theory (FFT) model coupled to the Elle modelling platform (www.elle.ws; Lebensohn 2001; Bons et al. 2008). The FFT-approach simulates visco-plastic deformation by dislocation glide, taking into account the different available slip systems and their critical resolved shear stresses in relations to the applied stresses. Griera et al. (2011; 2013) have shown that this approach is particularly well suited for strongly anisotropic minerals, such as mica and ice Ih (Llorens 2015). We modelled single- and polyphase composites of minerals with different anisotropies and strengths, roughly equivalent to minerals such as ice Ih, mica, quartz and feldspar. Single-phase polycrystalline aggregates show distinct heterogeneity of strain rate, especially in case of ice Ih, which is mechanically close to mica (see also Griera et al. 2015). Finite strain distributions are heterogeneous as well, but the patterns may differ from that of the strain rate distribution. Dynamic recrystallisation, however, usually masks any strain and strain rate localisation (Llorens 2015). In case of polyphase aggregates, equivalent to e.g. a granite, we observe extensive localisation in both syn- and antithetic shear bands. The antithetic shear bands are, however, ephemeral and best seen in movies. In the final microstructure they are very difficult to discern. We present movies that show that in all cases the distribution of both strain rate and of finite strain is much more heterogeneous than the finite microstructure tends to show. Bons, P.D., et al. (2008) Lecture Notes in Earth Sciences, 106 Griera, A. et al. (2011) Geology, 39, 275-278 Griera, A., et al. (2013) Tectonophysics, 587, 4-29 Griera, A., et al. Geotectonic Research, 97, 37-39 Lebensohn, R.A. (2001) Acta Materialia, 49, 2723-2737 Llorens, M.G. (2015) ) Numerical simulation of deformation microstructures and folds in polar ice and ductile rocks. PhD-thesis, Tübingen Univ. Llorens, M.G., et al. (in press) Journal of Glaciology

Description: Localisation of ductile deformation in rocks is commonly found at all scales from crustal shear zones down to grain scale shear bands. Of the various mechanisms for localisation, mechanical anisotropy has received relatively little attention, especially in numerical modelling. Mechanical anisotropy can be due to dislocation creep of minerals (e.g. ice or mica) and/or layering in rocks (e.g. bedding, cleavage). We simulated simple-shear deformation of a locally anisotropic, single-phase power-law rheology material up to shear strain of five. Localisation of shear rate in narrow shear bands occurs, depending on the magnitude of anisotropy and the stress exponent. At high anisotropy values, strain-rate frequency distributions become approximately log-normal with heavy, exponential tails. Localisation due to anisotropy is scale-independent and thus provides a single mechanism for a self-organised hierarchy of shear bands and zones from mm-to km-scales. The numerical simulations are compared with the natural example of the Northern Shear Belt at Cap de Creus, NE Spain.

Description: Creep due to ice flow is generally thought to be the main cause for the formation of crystallographic preferred orientations (CPOs) in polycrystalline anisotropic ice. However, linking the development of CPOs to the ice flow history requires a proper understanding of the ice aggregate's microstructural response to flow transitions. In this contribution the influence of ice deformation history on the CPO development is investigated by means of full-field numerical simulations at the microscale. We simulate the CPO evolution of polycrystalline ice under combinations of two consecutive deformation events up to high strain, using the code VPFFT (visco-plastic fast Fourier transform algorithm) within ELLE. A volume of ice is first deformed under coaxial boundary conditions, which results in a CPO. The sample is then subjected to different boundary conditions (coaxial or non-coaxial) in order to observe how the deformation regime switch impacts the CPO. The model results indicate that the second flow event tends to destroy the first, inherited fabric with a range of transitional fabrics. However, the transition is slow when crystallographic axes are critically oriented with respect to the second imposed regime. Therefore, interpretations of past deformation events from observed CPOs must be carried out with caution, particularly in areas with complex deformation histories.