The not-so-simple effects of boundary conditions on models of simple shear

Analog modeling of geological processes, such as folding instabilities or the behavior of inclusions in a matrix, often employs a linear simple-shear rig. In theory, a homogeneous plane-strain flow is prescribed at the boundaries of such deformation rigs but, in practice, the resulting internal deformation of the analog material (commonly paraffin wax or silicone putties) often deviates strongly from the intended homogeneous strain field. This can easily lead to misinterpretation of such analog experiments. We present a numerical finite-element approach to quantify the influence of imperfect simple-shear boundary conditions on the internal deformation of a homogeneous viscous analog material. The results demonstrate that imperfect boundary conditions in the vorticity-normal plane can cause the heterogeneous strain observed in some analog experiments. However, in other experiments, the analog material lies on top of a weak lubricating material or is sandwiched between two such materials. These layers lead to a viscous drag force acting on the analog material, resulting in imperfect simple-shear boundary conditions in the third dimension. For this experimental configuration, the numerical results show that the lubricating layers are responsible for the heterogeneous strain observed in analog models. The resulting errors in internal strain can be as high as 100%, and these difficult-to-avoid boundary effects must be considered when interpreting analog simple-shear experiments.