If the inhomogeneous simple shear proceeds under brittle ductile regime of deformation, structures like the sigmoidal extension veins as shown in the figure are produced. At the first small increment of deformation by heterogeneous simple shear, cracks are produced parallel to the maximum principal compressive stress or subperpendicular to the maximum stretch of the related finite deformation ellipsoid. These cracks or extension fissures are oriented at 45° to the direction of shear if the deformation is volume conserving. If not, the original angle may be greater than 45° if there is volume loss (with 1+e1 becoming closer to shear planes even at the onset of deformation) or less than 45° if there is volume gain (with 1+e1 getting away and closer to normal to shear planes even at the onset of deformation- see the figure at this link ). As the shearing progresses, the earlier formed extension fissures rotate towards the direction of shear and new cracks form again at 45° to the shear direction. But the process is through so infinitesimally small shear increments that the two are more or less continuous with the latest chords of the sigmoidal fissures showing the last of the incremental shears. As the cracks are produced, they are filled in by fibrous growth of quartz or calcite or chlorite, the crystal C axes being oriented parallel to the incremental 1+e1 at each stage and the fibrous growth itself has a sigmoidal form too. The crystal species is generally of a mineral that is commonly found in the wall rock or host rock. As a result of this sigmoidal extension fissures are formed, with sigmoidal crystal fibres within them. As the rock undergoes deformation generally by PRESSURE SOLUTION or SOLUTION TRANSFER (which works more or less on the lines of Le Chatlier's or PoyntingPrinciple), tectonic stylolites or spaced pressure solution striped cleavage may be produced subperpendicular to them or to the last stage chords of the veins. This is shown in the third stage of the deformation in the figure above. Needless to say, the pressure solution cleavage makes an angle of 135° with the direction of shear. But if the dilation is involved, the pressure solution seams make an angle greater ( volume loss) or lesser (volume gain) than 135° . The sense of sigmoidality helps in deducing the sense of shear (whether sinistral or dextral). The sigmoidality also helps in computing the incremental gamma values from the equation shown in the figure at this place. If there is volume change the incremental shear strain values could be computed from the equation given by Durney :
tan 2 q ' = d D / d g
where q ' is the angle that the chord of the vein makes with the walls of the shear zones. Below is shown a photograph of such veins produced in the Mahakoshal rocks (Archaean Proterozoic Boundary) near Barmhan in Central India. Note that the individual veins contain in nearly normal direction, fine cracks filled in by chlorite. These are incipient pressure solution seams. Parallel to the late stage chords are major cracks developed which are oriented parallel to the direction of the maximum principal compressive stress. The quartz infill is not fibrous though, the pristine condition has been destroyed by slightly higher metamorphism superimposed.