Rotation of prismatic rigid porphyroblasts and development of internal foliation: Results from pixel-based modelling study

We have modelled rigid-body rotation of growing prismatic porphyroblasts and development of internal foliation formed by capturing external foliation. Jefferey equations (1922) were used for the porphyroblast rotation with the assumptions that porphyroblasts are mechanically rigid objects embedded in a deforming ductile matrix. The growth rule applied in this model is a simple expansion of crystal faces with known Miller indices with the pre-assigned growth rate for each face. The external foliation is assumed to have constant orientation. Parts of external foliation within the calculated volume of a porphyroblast are captured during the growth and rotated with the porphyroblast once they are captured. During simple shear flow, prismatic porphyroblasts with every possible orientation with respect to the shear plane rotate constantly. The rate of rotation is determined as a function of strain rate and the shape and orientation of porphyroblasts. On the contrary, during pure shear flow, the longest axes of porphyroblasts approach toward the stretching direction. The observed patterns of the internal foliation within a porphyroblast are complicated in general, because the orientation of the rotation axis is not fixed with respect the kinematic reference frame. However, when there is pure shearing component in the flow geometry, porphyroblasts tend to have stable orientations and it is expected that Si patterns within a syntectonic porphyroblast can be straight. Thus, the straight Si patterns can be a good indicator for the flow geometry with some component of shear-direction-parallel stretching for syntectonic porphyroblasts. From the observations of model porphyroblasts, it is also proposed that central sections needs to be observed for the interpretation of internal foliations within prismatic porphyroblasts.