Three-dimensional angular shear deformation in finite elasticity

Angular shear deformations are based solely on the angular variation of line elements and not on their extension. To describe kinematics, a material cube is considered that transforms into an oblique prism, where two opposite faces are equal and parallel. Using the displacement components of three vertices of the fundamental edges, positioned along the reference axes, the displacement field of the body has been obtained. Then, the deformation tensors have been determined and some general properties for this class of shear deformations have been highlighted. Using a Lagrangian analysis, the boundary value problem for the equilibrium of a cube subjected to a purely angular shear deformation has been formulated. Subsequently, Piola-Kirchhoff and Cauchy stress tensors, together with the normal and tangential Cauchy stress vector components acting on the inclined faces of the deformed cube, have been evaluated.