Maps of the first principal strain rate (in units of inverse time step) during time step 50 for each of the four experiments. The brightness in each map is proportional to strain rate, overlaid by the grain boundary network as white lines. The same grey scale is used for all four maps. (a) Experiment A, showing a relatively homogeneous strain rate distribution, with a small amount of localization close to the small grain in the top-right (arrow). (b) Experiment B, showing a relatively homogeneous strain rate distribution, but with more intense localization close to the small grain in the top-right (arrow). (c) Experiment C, showing several subtle narrow horizontal zones of higher strain rate, which coincide with zones of finer grained material. (d) Experiment D, showing a broad sub-horizontal zone of high strain rate, which is in turn divided into narrow intense zones of deformation. These narrow zones coincide with zones of finer grained material. Brighter pixels reflect higher strain rates. 

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... processes were in- active. Fig. 3 shows an image of the input microstruc- ture, shaded according to each grain's area, and thus it also shows the variation in starting viscosities, since the starting strain state is the same in all grains. After 50 time steps, equivalent to a bulk shear strain of 2.5, a strong grain shape foliation has developed (Fig. 4a), and the variation in the first principal component of the strain rate tensor for the final time step is quite small, and mostly concentrated around one small (and hence weak) grain near the top of the sample. If we examine the shape of a deformed triangular mesh which originally had a square outline, and its equiv- alent restored to ...

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... this experiment the stress exponent was set to 3, however the two grain-size modifying processes were still inactive. We can see that after 50 time steps, a strong grain shape foliation has again developed (Fig. 4b), and the variation in the first principal strain rate for the final time step is slightly larger, still mostly concentrated around the same small grain. The de- formed mesh again shows the perturbation of the finite strain grid resulting from variations in the starting (grain-size dependent) viscosities of the grains (Fig. 5b), and ...

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... this experiment the stress exponent was set to 1, and now the two grain-size modifying processes were activated (Fig. 7). We can see that after 50 time steps the grain shape foliation is much weaker, as both the grain-size modifying processes have a tendency to pro- duce more equant grain shapes (Fig. 4c), and there has been a significant overall reduction in grain size. The variation in the first principal strain rate for the final time step is similar to that seen in Experiment B. The deformed mesh shows a small but distinct deflection of the grid near the centre of the sample (Fig 5c), which can be explained by a short lived period ...

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... this experiment the stress exponent was set to 3, and the two grain-size modifying processes were again activated (Fig. 8). We can see that after 50 time steps the grain shape foliation is much weaker, and there is a significant variation in grain sizes as well (Fig. 4d). The variation in the first principal strain rate for the final time step is much larger than in the previous experiments, and is concentrated around a narrow sub-horizontal band of high strain rate near the centre of the sample. The deformed mesh shows a strong but wider deflection of the grid also focused near the centre of the ...