The rotation rate of cylindrical objects during simple shear

The rotational behaviour of circular objects is modelled using a two-dimensional finite element simulation. We present results for linear and non-linear viscous rheologies and explore parameter space for the rheology contrast between object and matrix, η, and for object size relative to the shear zone width, L. For high η, our results confirm analytical descriptions for L→0 in that the rotation rate of the object is half of the bulk shear strain rate. However, we show that for 0.1>L<0.9, the rotation rate as a function of L can have a minimum, a maximum, or it can decrease or increase, depending on the stress exponent and η. In fact, for some rheologies, the rotation rate may decrease to <0.3 of the shear strain rate at intermediate L≈0.5 (≈20% area of porphyroblast in thin section). counter intuitive results have important consequences for the interpretation of the rotational behaviour of minerals in deforming rocks. For example, in rocks where garnet constitutes a volumetrically significant proportion of the bulk rock, the effective shear zone boundaries may be given by neighbouring crystals corresponding to intermediate L as described here. Thus, the interpretation of the rotation rate of crystals in such rocks can only be performed if the distance to the effective system boundaries is known.