Inhomogeneous Sliding Shear Versus Simple Shear in Linear Elasticity

The simplest possible shear deformation is obtained when a face of a block is displaced relative to its opposite parallel face. This sliding shear problem is physically different from the classic simple shear problem. In fact, simple shear produces a homogeneous deformation field, which is necessarily maintained by distributions of tangential stresses applied on the external faces of the block. By contrast, the deformation field generated by sliding shear is inhomogeneous, with the lateral faces of the block always remaining traction-free. Few studies have been conducted on the sliding shear, so it can be asserted that many questions related to this basic problem remain unresolved today. In this paper, the sliding shear problem is formulated within the framework of classical linear elasticity for isotropic materials. However, due to its mathematical complexity, only semi-analytical solutions are provided.