Pure shear deformation of square objects, and applications to geological strain analysis

Geological objects that deform differently from the rock matrix, such as pebbles or other clasts, are unlikely to have been originally circular or elliptical in section, and must therefore be expected to deform heterogeneously and change shape irregularly. We investigate this process with finite element models of pure shear deformation of square objects in three orientations, square, skew and diagonal, in a matrix with different viscosity. Modelling shows that 'squares' deform irregularly, with competent objects becoming barrel shaped and 'fish mouthed' (cf. boudins), whereas incompetent objects become bone shaped or elongate lobes. The object aspect ratios (R(O)) are less different from the bulk strain ratio (R(S)) than for equivalent circular objects. In contrast, diagonal squares deform almost homogeneously into 'rhombs', with aspect ratios closer to those for circles. Asymmetrically oriented 'skew squares' behave intermediately, developing skew flag and hooked shapes according to competence contrasts, that might be misdiagnosed as shear criteria. All these square objects (and circles in theory), show almost linear strain paths of object versus bulk (R - 1), with slope related to viscosity ratio, object shape and orientation. Linear relationships are also found for concavity/convexity shape factors for 'squares'. The results have implications for strain analysis and competence contrasts in rocks.