Numerical modelling and comparison of the temporal evolution of mantle and tails surrounding rigid elliptical objects in simple shear regime under stick and slip boundary conditions

Structures associated with rigid inclusions are a rich source of evidence to understand the local deformation regime. The behaviour of rigid objects in modelled here as being immersed in a linear Newtonian fluid with either (i) a stick boundary condition (continuity of stress and velocity across the boundary) or (ii) a slip boundary condition (continuity of boundary normal stress and velocity across the boundary with zero shear stress at the boundary). Of particular interest are the types of structures developed in a concentric region adjacent to the object termed the mantle. A model of the displacement of points around the inclusion comprises a set of ordinary differential equations which are solved numerically. A comprehensive set of simulations for a variety of mantle sizes, object aspect ratios, initial orientations as well as different boundary conditions has been performed. A comparison between natural examples and model output indicates a level of consistency. The resulting structures differ in detail and in a broader sense. In general δ-type structures only develop when stick boundary conditions are in operation. In contrast, σ-type structures at high strain are restricted to slip boundary conditions. Slip conditions also tend to be the source of complex mantle types involving more than one generation of mantle structures or wings. Furthermore, our model indicates that using asymmetry of orientation of objects relative to the shear direction may be problematic when used alone, particularly if stick boundary conditions prevail but that together with mantle structures there is less chance of confusion. •Model of mantle structures around rigid objects with stick and slip boundary conditions.•Numerical solution presented in graphical form.•Resulting structures differ in detail and in a broader sense between stick and slip cases.•Natural examples are comparable to model output.