Reorientation of inclusions by combination of pure shear and simple shear

Abstract

For a particular ratio of the rates of simultaneous pure shear to simple shear (s_r = /.ε //.γ), the rate of rotation or the finite angle of rotation of a rigid elliptical inclusion embedded in a viscous medium varies in a systematic manner depending on the orientation and the axial ratio (R) of the inclusion. Depending on whether R is less than or greater than, or is equal to (1+√1+4s_r²/2s_r, the minimum value of the rate of rotation can be positive, negative or zero. This would mean that in the same bulk deformation (with s_r ≠ 0), some inclusions may rotate in the same sense as the sense of rotation for the simple-shear component, while others in other orientations may rotate in the opposite sense, or may even remain stationary. Again, depending upon these critical relations, the total rotation for continuous deformation may be either indefinitely large or restricted. In the latter case (which occurs if R and s_r are not too small), the inclusions would tend to approach stable orientations, which, with increase in s_r will come fairly close to the direction of shear of the component of simple shear (x-axis). With increase in the axial ratio, the rotation of a rigid inclusion will rapidly approach that of a passive marker; a sufficiently long inclusion would rotate as a marker plane. At high angles to the x-axis, a longer inclusion rotates faster, the marker line being the fastest. At low angles to the x-axis a shorter inclusion rotates faster, the marker line being the slowest. At certain critical orientations (depending on s_r and R), all inclusions as well as the passive marker rotate at the same rate, viz.> g/2, which is also the constant rate of rotation of an equant inclusion. Theoretical and experimental studies of the varying rates of rotation of inclusions and passive markers give us a basis for understanding the course of evolution of certain geologic structures such as the en-echelon arrangement of boudins or drag patterns of foliation around rigid porphyroblasts. Certain aspects of the change in shape and orientation of non-rigid inclusions have also been studied in a qualitative manner.